Thermodynamics

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2-Week ISTE Workshopon

Engineering Thermodynamics

EXERCISES

U. N. GaitondeU. V. Bhandarkar

B. P. Puranik

Department of Mechanical EngineeringIndian Institute of Technology Bombay

December 11–21, 2012

201212071520

Engineering Thermodynamics – Exercises ii

Texts/References

There are a number of good books on Thermodynamics. An illustrative list is:

• M. Achuthan, ‘Engineering Thermodynamics’, Prentice-Hall of India, Second

Edition, New Delhi, 2009.

• M. J. Moran and H. N. Shapiro, ‘Fundamentals of Engineering Thermody-

namics’, Fourth Edition, Wiley, New York, 2000.

• F. W. Sears and G. L. Salinger, ‘Thermodynamics, Kinetic Theory and Sta-

tistical Thermodynamics’, Addison-Wesley/Narosa, New Delhi, 1975.

• R. E. Sonntag, C. Borgnakke, and G. J. Van Wylen, ‘Fundamentals of Ther-

modynamics’, Sixth Edition, Wiley, Singapore, 2003.

• M. W. Zemansky, ‘Heat and Thermodynamics’, Fourth Edition, McGraw-Hill

Kogakusha, New York/Tokyo, 1957.

Steam Tables

• M. L. Mathur and F. S. Mehta, ‘Steam and Other Tables (with Mollier Chart)’,

Revised Edition, Jain Brothers, New Delhi, 2010.

Engineering Thermodynamics – Exercises 1

The Work Interaction

WI.1 Two kg of a substance undergoes the specified process in a cylinder-piston

arrangement:

p1 = 6 bar; V1 = 0.2 m3; p2 = 2 bar; V2 = 0.6 m

3.

Determine the work done in each case.

(a) p varies as a linear function of V . (b) pV = a constant. (c) p remains

constant till the volume reaches 0.3 m3; pV n = a constant after that.

WI.2 An electric heater has a resistance of 50Ω. It is connected across a power

supply of 240 V, for a period of 2 hr. Determine the work done by the power

supply on the heater. How many ‘units’ of electricity are consumed?

WI.3 A system containing 5 kg of a substance is stirred with a torque of 0.3 kgf-m

at a speed of 1000 RPM for 24 hr. The system meanwhile expands from 1 m3

to 2 m3 against a constant pressure of 4 kgf/cm2. Determine the net work done

in kJ.

WI.4 Consider the situation shown in the figure below. The width of the channel

h

x

po

water

piston

is b, normal to the paper. The atmospheric pressure is p0.

(a) Show that the force exerted by the water on the piston is

F =

(

p0 +ρgh

2

)

hb,

where ρ is the density of water.

(b) Calculate the work done by the water on the piston and by the atmo-

sphere on the water when the chamber length is increased slowly from x1 to

x2. Express your answers in terms of p0, b, h1, x1, x2, ρ, and g.

WI.5 The pressure on a 250 g block of metal in increased quasi-statically and isother-

mally from 0 to 1000 bar. Assume that the density and isothermal bulk modu-

lus of the metal remain (almost) constant at 20.0 g/cm3 and 2×1012 dyne/cm2


respectively, determine the work done in J. Isothermal bulk modulus is defined

as B = −V (∂p/∂V )T .

WI.6 The tension in a wire in increased quasi-statically and isothermally from Fi to

Ff . If the length (L), cross-sectional are (A) and isothermal Young’s modulus

(Y ) remain (almost) constant, show that the work done by the wire is

W = −LF 2

f − F 2

i

2AY.

The Young’s modulus Y = (L/A)(∂F/∂L)T . Determine the work done if

L = 2 m, A = 0.0016 cm2, Fi = 10 N, Ff = 100 N, and Y = 2.0× 107 N/cm2.

WI.7 The equation of state of an ideal elastic substance is given by

F = KT

[

L

L0

−L2

0

L2

]

,

where K is a constant and L0 (the length at zero tension) depends only on

T . Calculate the work necessary to compress the substance from L = L0 to

L = L0/2, quasi-statically and isothermally.

WI.8 (a) Show, from first principles, that when the surface area of a system, subject

to a surface tension σ, changes by a small amount dA, the work done by the

system is (−σdA). (b) A bubble rose from the bottom of a lake to near its

surface. The bubble was initially 1 cm in diameter, at a pressure of 2 bar. The

final pressure experienced by the bubble was 1 bar. The initial as well as the

final shape of the bubble was spherical, and its volume varied inversely to the

pressure. Determine the net work done by the bubble. For water, σ = 0.073

N/m. Which additional assumptions did you make? Please comment on your

answer.

Additional Exercises

Achuthan, Chapter 3: Problems 6, 7, 9, 14-21 (pp 68–73).

Moran and Shapiro: Problems 2.18 to 2.45 (pp 75–77). Some of these use

non-metric units, you may convert these to metric/SI units.

Sears and Salinger: Problems 3-1 to 3-3, and 3-6(p90).

Sonntag et al.: Problems 4.20 to 4.94 (pp 106–111).


The First Law – 1

F1.1 A system executes a quasi-static process from an initial state 1 to a final state

2, absorbing 80 kJ of heat and expanding from 2.0 m3 to 2.25 m3 against a

constant pressure of 1.5 bar. The system is brought back to its initial state by

a non-quasi-static process, during which it rejects 100 kJ of heat. What is the

work done during the second process?

F1.2 Three kg of air in a rigid container changes its state from 5.0 bar and 75C to

12 bar while it is stirred. The heat absorbed is 195 kJ. Assume air to be an

ideal gas with cv = 0.714 kJ/kg K. Determine the final temperature, change

in internal energy and work done.

F1.3 Two kg of air at 2.5 bar and 30C forms a closed system. It undergoes a

constant pressure process with heat addition of 450 kJ. Compute final temper-

ature, change in enthalpy, change in internal energy, and work done. Assume

air to be an ideal gas, with MolWt of 29 kg/kmol and cv = 0.714 kJ/kg K.

F1.4 A perfectly insulated system contains 0.1 m3 of hydrogen at 30C, 5.0 bar. It

is stirred at constant pressure till the temperature reaches 60C. Determine

heat transferred, change in internal energy, stirrer work, and net work. Treat

hydrogen as an ideal gas with MolWt = 2 kg/kmol, γ = 1.4.

F1.5 A closed system contains 2 kg of air at 3 bar, 150C. It is stirred, and expands

till its pressure reduces to 1 bar. During the process, the temperature of the

system is maintained constant at 150C. If the stirrer does 120 kJ of work,

determine (a) expansion work done, and (b) heat transferred. Assume R =

287 J/kg K for air.

F1.6 The heat transferred during the quasi-static process of an ideal gas with con-

stant specific heats in which only expansion work is done can be represented

by dq = c dT , where c is a constant. Show that the equation for this process

can be represented as p vk = const. Determine k in terms of cp, cv and c.

F1.7 Consider the action of an air gun. The gun consists of a chamber of volume

VC connected to a long cylindrical barrel of volume VB. Initially, compressed

air at pressure pC and temperature TC is filled in the chamber. The bullet is

located at the chamber-end of the barrel, and is held in place by a stopper.

When the bullet is relased, the air in the chamber expands into the barrel

and accelerates the bullet. Assume that the bullet behaves like a leak-proof,

frictionless piston; air expands adiabatically; and air behaves like an ideal

gas with constant specific heats. (a) Obtain an expression for V0, the muzzle


velocity of the bullet, in terms of pC , VB, VC , mb (mass of the bullet), and po

(ambient pressure). (b) Is there an optimal length of the barrel? (c) In what

way, in a real air-gun, will the situation differ?

F1.8 Consider the electrolyte in a car battery as a system. It is charged over a period

of 24[h]. During charging, the potential across the electrodes is 24[V] and the

current drawn is 1.0[A]. During the process, 15.0[litre] of a gas is evolved. The

evolution of gas may be modeled as the displacement of the atmosphere, which

remains at 1.0[bar]. (a) Sketch the system diagram. (b) Sketch appropriate

process diagrams. (c) Determine all components of work done by the system,

and the total work.

F1.9 Argon (MolWt 40 kg/kmol) is initially at 4 bar, 100C in a closed system.

During a process, it expands from an initial volume of 10 litre to a final volume

of 20 litre. The final pressure is 2 bar, and the process may be represented by

a straight line on a p–V diagram. During the process, the system is stirred,

and absorbs 3 kJ of stirrer work. Determine expansion work, total work, and

heat absorbed by the system.

F1.10 Two kg of Nitrogen gas, initially at 10 bar, 400 K, executes an adiabatic

process to 5 bar, 200 K. The process is suspected to be non-quasi-static.

During the process the system absorbs electric work of 1500 kJ. Determine

(a) change in volume, (b) change in internal energy, (c) change in enthalpy,

(d) net work done, and (e) expansion work done. For Nitrogen, molecular mass

is 28 kg/kmol and γ = 1.4.

F1.11 A closed contains 10 kg of an ideal gas. The initial state is 10 bar, 300 K,

and the final state is 5 bar, 300 K. The process is not necessarily quasi-static.

During the process, electric work of 50 kJ is absorbed, and the heat loss is

30 kJ. Sketch the process on a p–V diagram. Determine (a) change in energy,

(b) expansion work, (c) total work.


Achuthan, Chapter 5: Problems 1(p103), 5, 6(p104), 7, 8, 11(p105), and 12,

13(p106).

Moran and Shapiro: Problems 2.54 to 2.70 (pp 78–80). Some of these use

non-metric units, you may convert these to metric/SI units.

Sears and Salinger (Read ‘quasi-static’ where you see ‘reversible’.): Problems

2-4(p55)+3-4(p90) 2-5(p55)+3-5(p90), 3-7(p90), 3-13 to 3-18(pp91,92), 3-22

to 3-26(p93)

Sonntag et al.: Problems 5.89 to 5.102(pp 152–154).


Properties of Fluids, The First Law – 2

F2.0 Plot, using your steam tables, the following diagrams for ordinary water sub-

stance.

(a) p–v diagram on linear scales. Plot a number of isotherms.

(b) p–v diagram on logarithmic scales. Plot a number of isotherms.

(c) u–T diagram on linear scales. Plot a number of isobars.

(d) h–T diagram on linear scales. Plot a number of isobars.

(e) T–v diagram, linear scale for T , logarithmic scale for v.

(f) T–s diagram on linear scales. Plot a number of isobars.

F2.1 Find the state of a closed system containing 1 kg of water substance as men-

tioned below. Specify h, v, x, and s as appropriate:

(a) saturated liquid at 5 bar,

(b) saturated vapour at 10 bar,

(c) wet steam of quality 0.8 and at 3 bar,

(d) 5 bar, 200C, and

(e) 100 bar, 200C.

F2.2 Classify the following states of 1 kg of water substance as wet, dry saturated,

superheated steam, subcooled liquid, etc.:

(a) p = 1 bar, T = 150C, (b) p = 2 bar, T = 200C,

(c) p = 2 bar, S = 6.2 kJ/K, (d) p = 2 bar, V = 0.1 m3,

(e) H = 2900 kJ, S = 6.2 kJ/K, (f) H = 2500 kJ, S = 8.8 kJ/K,

(g) H = 2700 kJ, p = 0.5 bar, (h) H = 2100 kJ,T = 50C,

(i) T = 100C, x = 0.8.

F2.3 For the following processes, find the changes in h, s, v, T , and x, as appropriate.

The initial state pressure is p1 = 5 bar. the final state is 2.

(a) constant volume : v1 = 0.3 m3/kg, p2 = 3.0 bar;

(b) constant entropy : s1 = 6.3 kJ/kg K, p2 = 1.5 bar;

(c) constant volume : h1 = 2500 kJ/kg, p2 = 2.0 bar;

(d) constant enthalpy : s1 = 6.4 kJ/kg K, p2 = 2.0 bar;

(e) constant volume : T1 = 200C, p2 = 2.0 bar;

(f) constant pressure : x1 = 0.5, T2 = 400C.

F2.4 For the Van der Waals equation of state,

(p+a

v2)(v − b) = RT


show that pc = a/27b2, vc = 3b, and Tc = 8a/27bR, where subscript c denotes

critical conditions.

F2.5 Derive the reduced equation of state for a Van der Waals gas:

(pR +3

v2R)(3vR − 1) = 8TR

where the the reduced quantities are defined as follows:

pR = p/pc, vR = v/vc, and TR = T/Tc.

F2.6 Obtain an equation for the expansion work done by a Van der Waals gas during

an isothermal process in terms of the reduced quantities.

F2.7 Determine the region of p–v–T space in which a Van der Waals equation can

be approximated by an ideal gas equation to an accuracy of ±1% in pressure.

(That is, |(pvg − pig)/pig| ≤ 0.01, where pvg and pig are pressures calculated

using the Van der Waals equation and the ideal gas equation, respectively, at

the same v and T .)

F2.8 From the steam tables, read off the critical conditions for water substance.

Obtain the Van der Waals constants a and b.

F2.9 Show that, for a Van der Waals gas, pc vc /RTc = 3/8. Check this out for

steam. How good is the Van der Waals equation for steam? Comment.

F2.10 Calculate the work done per kg in compressing steam (a) from 1 bar to 25 bar,

isothermally at 400C, and (b) from 5 bar to 25 bar, isothermally at 600C. Use

steam tables and the trapezoidal rule for integration. Compare these values

with those obtained by assuming steam to be a Van der Waals gas.

F2.11 Two kg of steam at critical conditions is sealed in a rigid container. It is then

placed inside an oven at 349.9C, and allowed to reach thermal equilibrium.

Determine the masses of water and steam in the final state, and the heat

transferred.

F2.12 2 kg of saturated liquid water at 12 bar is mixed with 1 kg of superheated

steam at 12 bar, 300C. The mixing is adiabatic and at constant pressure.

Determine the changes in volume and internal energy, the dryness fraction in

the final state, and work done.

F2.13 Compute the changes in the internal energy and enthalpy, and the expansion

work done when 1 kg of saturated liquid water at 100C evaporates isothermally

into dry saturated steam.


F2.14 Water at 100C and 6 bar is supplied 1500 kJ/kg of heat at constant pressure.

Determine the final state of the system (enthalpy, dryness fraction, tempera-

ture). The system is a closed one.

F2.15 A rigid metallic container is separated into two equal parts by a thin partition.

One part contains 1 kg of saturated liquid water at 100C. The other part is

evacuated. The partition is broken, and equilibrium reestablished after some

time. During the process, the temperature of the system is maintained by

immersing it in an oil bath maintained at 100C. Determine (a) final state of

steam, (b) work done, and (c) heat transferred.

F2.16 Consider the system shown in the figure. The left chamber contains an ideal

gas. The right chamber contains 2 kg of saturated liquid water at 1 bar.

The gas is sirred, and the steam allowed to expand at constant pressure till

it becomes dry saturated. Determine (a) change in internal energy of the

ideal gas, (b) heat transferred across the diathermal wall, (c) stirrer work, and

(d) work done by steam.

gasideal

2 kg water

adiabatic cylinder

p=constant

adiabatic piston

stirrer

fixed diathermic partition

Rework the problem if the stirring is continued till the the steam reaches a

temperature of 150C. Assume that the ideal gas has a mass of 1 kg, and its

specific heat at constant volume is 0.72 kJ/kg K.

F2.17 A rigid, insulated vessel is divided into two chambers by an adiabatic partition

wall. One chamber contains 1 kg of wet steam at 4 bar and dryness fraction

0.7, while the other chamber contains 0.5 kg of dry saturated steam at 2 bar.

If the partition between the chambers is removed, and the fluids on both sides

allowed to mix, determine the specific volume, specific internal energy, pressure,

and dryness fraction in the final state. (You may have to use a trial-and-error

procedure, or a graphical procedure, to determine the final state.)

F2.18 1.5 kg of steam is compressed from an initial state 1 (2 bar, dry saturated)

to a final state 2 (8 bar). The process may be modeled as pV = constant.

Determine (a) final temperature and final state, (b) change in energy, (c) work

done by steam, and (d) heat absorbed by steam.


The Second Law

Whenever you work with the Second Law, keep the following questions in mind:

Does the process satisfy the Second Law? Is it impossible, reversible, or irreversible?

If irreversible, what are the causees of irreversibility?

SL.1 A conductor connects two reservoirs at temperatures of 1200 K and 500 K. The

steady flow rate of heat from the hot to the cold reservoir is 150 W. Determine

the rate of entropy production by the conductor.

SL.2 1 kg of water in a cylinder-piston arrangement is initially in the saturated

liquid state at 8 bar. It absorbs heat from a reservoir at 250C. During the

process the piston moves in such a way that the pressure remains constant. At

the end of the process, water has completely evaporated into steam. Determine

(a) heat transferred, (b) change in entropy of the system, (c) change in entropy

of the reservoir, and (d) change in entropy of the universe.

SL.3 A thermally insulated cylinder, closed at both ends, is fitted with a leakproof,

frictionless, diathermic piston which divides the cylinder into two parts. Ini-

tially, the piston is clamped in the centre, with 1 litre of air at 300 K and

3 bar on one side and 1 litre of air at 300 K and 1 bar on the other side. The

piston is released, and reaches equilibrium in pressure and temperature at a

new position. Compute the final pressure and temperature and the change in

entropy. Which irreversible process has taken place?

SL.4 Three kg of an ideal gas in a rigid insulated container changes its state from

600 kPa and 300 K to 2 MPa, while it is stirred. Assuming cp 1.0 kJ/kg K,

and γ = 1.4, determine the change in entropy of the system.

SL.5 An insulated chamber of volume 2V0 is divided by a thin, rigid partition into

two parts of volume V0 each. Initially, one chamber contains an ideal gas

at a pressure p0 and temperature T0. The other chamber is evacuated. The

partition is suddenly removed. Show that, when equilibrium is reestablished,

the temperature is T0. Determine the change in entropy. Which irreversible

process has taken place?

SL.6 Ten kg of dry saturated steam at 35 bar, contained in a cylinder-piston ar-

rangement, is brought into thermal contact with a heat sink at 175C. The

steam rejects 16000 kJ of heat during a constant pressure process. Determine

(a) final state of steam, (b) change in entropy of steam, and (c) change in

entropy of the universe.


SL.7 Two kg of saturated liquid water at 2 bar is mixed adiabatically with 5 kg

of steam at 2 bar, 400C. During the process, the pressure remains constant.

Determine the final state and the change in entropy.

SL.8 One kg of a liquid at 300 K is mixed with 1 kg of the same liquid at 400 K

in an adiabatic calorimeter. Assume that there is no change of phase and that

the density and specific heat of the liquid remains constant at 1200 kg/m3 and

5 kJ/kg K. Calculate the change in entropy of the system.

SL.9 One kg of an ideal gas at 12 bar and 500 K is mixed with 1 kg of the same gas

at 5 bar and 300 K. The mixing takes place at constant volume. During the

process, the system rejects 150 kJ of heat to the environment, which remains

at 300 K. Gas properties: RMM = 32, γ = 1.33. Determine (a) final state

(temperature, volume, pressure), and (b) change in entropy of the universe.

SL.10 A closed system undergoes a process between fixed initial and final states

(1 and 2) such that the overall changes in energy, entropy, and volume are

E2−E1 = ∆E, S2−S1 = ∆S, and V2−V1 = ∆V respectively. The only input

of energy to the system is from condensing steam at a temperature Ts. The

only outputs of energy are the heat transfer to the environment and work done

in displacing the environment. The amount of heat absorbed from steam by

the system is Q. (a) Apply the first law to the system. (b) Apply the second

law to the system. (c) Show that any irreversibility in the process gives rise to

a wastage of the thermal energy of steam by an amount

Q−Ts

Ts − To

(∆E + po∆V − To∆S)

where po and To are respectively the pressure and temperature of the environ-

ment.

SL.11 An inventor has proposed a refrigeration system that works without any work

input. The invention has the following characteristics: (a) It is a cyclic device,

and does not have any work interaction with the surroundings. (b) It absorbs

35 kW of heat from the cold space at 10C, and also absorbs 90 kW of heat

from condensing steam at 100 C. (c) It rejects heat to the atmosphere, which

is at 30C.

Apply the first law and determine the rate of heat rejection to the atmosphere.

Apply the second law and determine whether the proposed system is possible

or not.

SL.12 Water in a piston cylinder assembly is as shown in the figure below. There are

two stops, a lower one at which the volume enclosed is 1 m3 and the upper one

at which the volume enclosed is 3 m3. The piston mass and the atmospheric


pressure are such that the piston floats at 500 kPa. The above described system

has water initially at 1 MPa and 500C. This is allowed to cool to 100C, by

rejecting heat to atmosphere at 30C. Calculate the total entropy generated in

the process?

Water

SL.13 Consider the system shown in the figure. The adiabatic cylinder(C)-piston(P)

arrangement has a fixed diathermic partition(D) inside it. The chamber away

from the piston(A) contains M kg of an ideal gas, initially at a temperature T1

and pressure p1. The other chamber(B) also contains M kg of the same gas,

initially at a temperature T1 and pressure p1.

C

P D

AB

During a process, the piston is moved slowly, to compress the gas in B. The

process continues till the temperature reaches T2. Determine (a) final pressure

of gas in A, (b) heat transfer across the partition D, (c) work done by gas in

B, (d) the entropy change of the universe, and (e) final pressure of gas in B.

(f) Show that the process for the gas in B can be represented by pvk = constant,

and obtain an expression for k in terms of γ of the gas.


Achuthan, Chapter 7: 6–9, 11, 12, 17 (pp 165–168).

Moran and Shapiro: 5.1 to 5.23 (pp 231–233).

Sears and Salinger: 5-1, 5-4, 5-5, 5-7 to 5-9, 5-11, 5-13, 5-16, 5-20, 5-21, 5-27

(pp141–145).

Sonntag et al.: 7.33 to 7.38 (p 242).


Property Relations

PR.1 Consider s as a function of T and p. Show that

T ds = cp dT − T

(

∂v

∂T

)

p

dp

PR.2 Now consider s as a function of T and v, and derive another expression for

T ds, similar to that in Exercise PR.1.

PR.3 Using the results of Exercises PR.1 and PR.2, show that

cp − cv = T

(

∂v

∂T

)

p

(

∂p

∂T

)

v

PR.4 Derive an expression for (∂cv/∂v)T in terms of p, v, and T .

PR.5 Show that for a Van der Waals gas, cv is a function of T alone.

PR.6 Determine cp − cv for a Van der Waals gas.

PR.7 Determine whether cp is a function of T alone for a Van der Waals gas.

PR.8 Using the table below, estimate the values of cp, cv, γ,

β =1

v

(

∂v

∂T

)

p

, κ = −1

v

(

∂v

∂p

)

T

, and α = −1

v

(

∂v

∂p

)

s

for steam at 7 bar and 500C.

p, bar T , C h, kJ/kg v, m3/kg s, kJ/kg K

7.0 490 3460 0.5002 7.901

7.0 500 3482 0.5069 7.929

7.0 510 3503 0.5136 7.957

6.5 500 3482 0.5461 7.964

7.5 500 3481 0.4730 7.897

PR.9 The Joule-Kelvin coefficient µ is defined as µ = (∂T/∂p)h. Show that

µ =1

cp

[

T

(

∂v

∂T

)

p

− v

]

What is the utility of this equation? Show that the Joule-Kelvin coefficient of

an ideal gas is zero.

PR.10 Prove that(

∂u

∂p

)

T

= −T

(

∂v

∂T

)

p

− p

(

∂v

∂p

)

T


PR.11 Prove that(

∂p

∂T

)

s

=cp

Tvβ

Describe an experiment that will use this relation to determine cp without any

energy measurements.

PR.12 In a property table, three consecutive entries at constant pressure are as

follows:1 2 3

h, kJ/kg 3465 3486 3508

s, kJ/kg K 8.329 8.356 8.384Estimate the value of temperature and specific Gibbs function at point 2.

PR.13 Determine gf and gg for ordinary water substance at 1 bar, 10 bar, 100 bar,

etc. Generalise the result. Explain it.

PR.14 For a fluid, the specific Gibbs function g(= h−Ts) is given by the expression

g = RT ln(p/p0)− b(T )p, where R and p0 are constants and b(T ) is a function

only of T . For such a fluid, (c) derive the equation of state, (d) an expression

for s, and (e) an expression for cp.

PR.15 Derive an expression for

(

∂T

∂v

)

u

in terms of cv, and EoS information.

Check its value for an ideal gas. Explain the result. Now, consider the case of

a Van-der-Waals gas. Comment on the result.

PR.16 The velocity of sound c in a fluid is related to the thermodynamic state by

the relation

c2 =

(

∂p

∂ρ

)

s

Express c2 in terms of cp, cv, p, ρ, and T . What does this expression reduce

to for an ideal gas with constant specific heats?

PR.17 Derive the Clausius-Clapeyron equation by applying Maxwell’s equation for

(∂T/∂p)v or (∂T/∂p)s in the two-phase zone of a fluid like water.

From the textbooks you have used, find out other methods to derive the C-C

equation.

Using Steam Tables, check whether the Clausius-Clapeyron equation is satis-

fied by steam-water equilibrium data at 100 bar.

PR.18 Consider a Carnot cycle working between two temperatures T and T − dT

with a vapour as a working fluid. The cycle lies entirely within the two-phase

zone of the vapour. Sketch the cycle on T − s coordinates. Write down an

expression for its efficiency, in terms of the work done and the heat absorbed.


Equate this to the standard expression for the efficiency of the Carnot cycle.

Hence, derive the Clausius-Clapeyron relation for (dT/dp)sat.

PR.19 he following relation between the saturation pressure p and saturation tem-

perature T of a fluid has been obtained by using the Clausius-Clapeyron equa-

tion.

ln p = A−hfg

RT,

where A is a constant. One of the assumptions made for this derivation is that

dry saturated vapour behaves like an ideal gas. Derive this equation. Which

additional assumptions did you make?

PR.20 If the specification for the properties of a substance is given as

a(T, v)

show that all its properties, including any change-of-phase (saturation) lines,

can be derived.

PR.21 Consider a Van-der-Waals gas, with a constant cv (note: you must have

already shown that cv for such a gas is a function of T alone). Obtain an

expression for a(T, v). It is recommended that you work with reduced prop-

erties. Use some reasonable values for cv and show, numerically/graphically,

that there exists a critical point, and determine some saturation points and

saturation states below critical temperature.

Open Thermodynamic Systems

OS.1 Joule postulated that the temperature of water when it comes down a waterfall

rises. Consider the waterfall to be an open thermodynamic system and deter-

mine the height through which the water should fall for its temperature to rise

by 1C. Assume water to be an incompressible fluid with cp = 4.186 kJ/kg K.

List all other assumptions made while solving the problem.

OS.2 Steam is supplied to a turbine with hi = 3.2 MJ/kg and it leaves with

he = 2.5 MJ/kg. The entrance and exit velocities are 170 m/s and 280 m/s

respectively. If the heat loss is 50 kJ/kg, what is the work done?

OS.3 A steady flow system receives 60 kg/min of gas at 2 bar, 90C with negligible

velocity, and discharges it at a point 20 m above the entrance section at a

temperature of 300C with a velocity of 2200 m/min. During this process,

2 kW of heat is supplied from external sources, and the increase in enthalpy is

7.8 kJ/kg. Determine the power output.


OS.4 A centrifugal air compressor compresses 5 m3/min of gas from 10 N/cm2 to

70 N/cm2. The inlet and exit specific volumes are 0.8 m3/kg and 0.4 m3/kg

respectively. The duct diameter is 10 cm at the inlet and 5 cm at the exit.

Determine (a) rate of flow work, (b) mass flow rate, and (c) change in velocity.

OS.5 A steam turbine receives steam at a rate of 5400 kg/hr and develops power of

600 kW. Neglecting heat losses, determine the change in specific enthalpy of

steam flowing through the turbine if (a) the entrance and exit velocities and

heights are negligible, and (b) if the entrance and exit velocities are 50 m/s

and 320 m/s respectively, and the inlet is 4 m above the exhaust.

OS.6 In a steady-state apparatus, the work done by the system is 80 kJ/kg of fluid.

The specific volume, pressure, and velocity at the inlet and exit are 0.5 m3/kg,

8 bar, 12 m/s, and 0.7 m3/kg, 1 bar, 220 m/s respectively. The inlet is 10 m

above the exit and the total heat loss is 10 kJ/kg of fluid. What is the change

in specific internal energy?

OS.7 A ship propulsion system incorporates a compressor which receives steam at

3.4 bar with 5 percent moisture. It delivers it dry and saturated at 8 bar.

Steam flow rate is 5 kg/s. The compression is adiabatic. Diameters of the

inlet and exit ducts are 20 cm. The mechanical efficiency of the machine is

92%. (a) Determine the power required to drive the compressor. (b) Is the

process possible or impossible? Why? What is the limiting exit state? Assume

that the exit pressure is fixed.

OS.8 The inlet conditions for the nozzle of a steam turbine are 60 bar, 350C. The

exit conditions are 10 bar, 0.9 dry. (a) If the steam flow rate is 10,000 kg/hr,

determine the exit velocity and exit area. (b) Is the process possible or impos-

sible? Why? What is the limiting exit state and exit velocity? Assume that

the exit pressure is fixed.

OS.9 The inlet conditions of a water pump are 1 bar, 25C, and the exit pressure

is 180 bar. The pump consumes 75 kW of power and pumps 12,000 litres of

water per hour (at inlet conditions). Determine the temperature of water at

the exit of the pump. If we define the ideal pump as the one which does the

pumping isothermally, what is the efficiency of the pump?

OS.10 Feedwater at 0.1 bar is pumped from a condenser into a boiler at 25 bar.

Water at the exit of condenser is saturated and the compression is isentropic.

Determine the work done per kg of water pumped, and the flow work.

OS.11 Water at a rate of 120 kg/min enters a pump at 1 bar, 35C. Thepump power

is 110 kW, and the pump raises the pressure to 5 bar. The water then passes


through a boiler in which 1800 kJ/kg of heat is added. Assuming negligible

pressure drop in the boiler, determine the state at the exit of the boiler and

the velocity at that point if the diameter of the exit duct is 20 cm.

OS.12 Water flows through a horizontal venturimeter at a steady rate of 600 kg/min.

The inlet and throat diameters of the venturi are 6.0 cm and 3.0 cm respectively.

If there is no transfer of heat or work, and no change in internal energy, and

if the density remains constant at 1000 kg/m3, what will be the pressure drop

between the inlet and throat in bar?

OS.13 Wet steam at 10 bar is passed through a throttling calorimeter. The state

of steam after throttling is 0.75 bar, 100C. What is the dryness fraction of

steam before throttling?

OS.14 A rigid, insulated bottle of volume V0 is perfectly evacuated. The stopper is

opened and ambient air (at p0, T0) is allowed to flow in. When the flow stops,

the stopper is replaced. Determine the final temperature of air in the bottle.

OS.15 Steam enters the nozzle of a steam turbine with a velocity of 5 m/s at a

pressure of 40 bar and 600C. The pressure and temperature at nozzle exit were

measured as 1 bar, 200C. Determine (a) exit velocity, (b) entropy production

rate if the flow rate of steam is 1.5 kg/s, and (c) isentropic efficiency of the

nozzle.

OS.16 An adiabatic steam turbine handles 10 kg/s of steam. The inlet state is

10 bar, dry saturated. The exit pressure is 1 bar. The isentropic efficiency of

the turbine is 0.8. Determine (a) exit state, (b) power output, and (c) entropy

production rate.

OS.17 In a heat exchanger, air is heated from 30C to 80C by means of a second

air stream which enters the heat exchanger at 150C. Both streams have a

flow rate of 2 kg/s and flow without any loss of pressure. Determine (a) heat

transferred between the streams, and (b) entropy production rate. Assume

cp = 1.0 kJ/kg K for air.

OS.18 120 kg/hr of saturated water at 8 bar enters a heat exchanger and leaves

at 4 bar, 200C. Hot air enters at 600C, 2 bar, and leaves at 240C, 2 bar.

Determine (a) flow rate of air, (b) heat transfer rate from air to water, (c) rate

of entropy outflow for each stream, and (d) entropy production rate. Use

cp = 1.0 kJ/kg K for air.

OS.19 An adiabatic cylinder C consists of two parts A and B, separated by a fixed,

diathermic, partition D as shown in the figure below:


A B

C

D

m

The chamber at the left is continuously flushed with dry saturated steam at

a pressure pA, and hence is initially full of it. The right chamber is now filled

with an ideal gas (with constant specific heats at a temperature TB which is

lower than TA(= Tsat(pA)). Heat is transferred across the diathermic partition

from steam to air, and the temperature of air finally reaches TA. Any steam

which condenses remains in chamber A (i.e. the exit state of A is always dry

saturated steam at pA).

(a) Explain, with appropriate equations, how you will determine (1) the heat

transferred across the partition, (2) the mass of condensed steam in chamber

A, and (3) the change in entropy of air in B. (Nomenclature: mB: mass of air

in B, cp, cv, γ: properties of air in B, m1: initial mass of steam in A, mg: final

mass of steam in A, mf : final mass of water (condensate) in A, hf , hg, hfg:

properties of steam.)

(b) Compute the quatities specified in (a) if pA = 40 bar, TB = 30C, and mB =

10 kg.

OS.20 The figure below shows a butane cylinder of diameter D = 0.4 m and height

H = 0.8 m. The butane is at 300 K. Initially, the level of liquid in the

cylinder in 0.7 m. The valve is opened, and some butane is taken out for

consumption. During this process, (a) the temperature of butane is maintained

at 300 K, (b) it absorbs heat from the environment, which is at 310 K, and

(c) only dry saturated vapour leaves the cylinder. The final level of butane

is 0.3 m. Determine the mass of butane consumed, and the heat absorbed.

Butane properties at 300 K are: psat = 2.607 bar, ρf = 570.5 kg/m3, ρg =

6.559 kg/m3, hf = 564.0 kJ/kg, hg = 924.7 kJ/kg.


vap

liq

D

H

OS.21 Cold air at 0C and 1 bar, and a flow rate of 1 kg/s is mixed with a hot

stream of air at 80C and 2 bar to provide warm air at 25C and 1 bar. The

mixer is an adiabatic open system with rigid walls. Determine (a) flow rate of

hot air, and (b) rate of entropy production. (c) Which irreversible process has

taken place?

OS.22 A throttling and separating calorimeter is used to measure the dryness frac-

tion of steam flowing through a duct at 10 bar.

wet

steam,10

bar Throttle

Separator

B, 1 bar, xB = 0, mB = 0.1 kg/s

A, 1 bar, xA = 1, mA = 0.9 kg/s

A sample of steam is throttled to near ambient temperature, and then put

through a separating chamber, where it is split into two streams. Stream A is

dry saturated steam and stream B is saturated liquid. The flow rates of the two

streams are measured as mA = 0.9 kg/s and mB = 0.1 kg/s. (a) Determine the

dryness fraction of steam in the duct. (b) Can a simple throttling calorimeter

be used for this measurement? Why?

OS.23 An incompressible liquid (density ρ, isobaric sp heat cp) of mass M is filled in

a tank, at an intial temperature T0. The top surface is open to the atmosphere

(at p0). For t ≥ 0, a stream of the same fluid enters the tank at a temperature

Ti, the inflow rate is mi. At the same time, fluid at a rate of me is withdrawn

from the tank. Assume that the liquid in the tank is well mixed and neglect

any heat transfer between the liquid and the surroundings. Derive expressions

for (a) rate of change of temperature of the liquid in the tank at t = 0, and

(b) rate of entropy production at t = 0.


OS.24 Study the figure shown below. The pump P pumps water into the boiler B.

The steam generated runs a turbine T. The exhaust of the turbine is split into

two streams 5 and 6 in the separator S. The mixer M is used to mix some water

from boiler inlet and some steam from boiler exit to provide a mixed steam 9.

Data: State 1: 1 bar, sat.liq.; States 2, 8: 50 bar; States 3, 7: 50 bar, 400C;

State 4: 2 bar; State 5: 2 bar, sat.liq.; State 6: 2 bar, dry.sat.vap.; State 9:

50 bar, dry.sat.vap.; m4 = 10 kg/s; m9 = 1 kg/s; isentropic efficiency of turbine

0.8. Determine (a) power produced by the turbine, (b) mass flows at 5, 6, 7,

8, and 1, (c) power comsumed by the pump, (d) rate of heat absorption in the

boiler, and rate of production of entropy in (e) the turbine, (f) the separator,

and (g) the mixer.

P B

M

1 2 3

4

56

78

9

Qb

Wt

T

S

Combined First and Second Laws

Assume that the environment is at p0 = 1 bar, T0 = 300 K, unless specified other-

wise.

CL.1 What is the maximum work that can be obtained from a perfectly evacuated

space of volume Vvac?

CL.2 Determine the maximum useful work that can be obtained when the following

systems undergo the specified change of state:

(a) 1 kg of ordinary water substance at (i) 10 bar, saturated liquid, (ii) 10 bar,

dry saturated vapour, (iii) 10 bar, 600C. In each case, the final state is (p0, T0).

(b) Initial state: Two identical systems of the same mass m, and specific heat

capacity cp, temperatures TA and TB, and pressure p0. Final state: equilibrium

with each other. Process: no change of phase, adiabatic, constant pressure.

CL.3 (a) Calculate the maximum useful power output from an adiabatic steam

turbine if the inlet state is 10 bar, 350C, exit pressure is 1 bar, and the flow


rate 5 kg/s. Also determine the exit state. (b) Rework the problem if the

steam loses 40 kJ/kg of heat to the atmosphere which is at 300 K. What is the

exit state in this case?

CL.4 Air at 1200 K and 8 bar expands in an adiabatic turbine to 1 bar, with an

isentropic efficiency of 0.85. The air flow rate is 2 kg/s. Determine (a) power

output, (b) maximum possible power output for the same inlet and exit condi-

tions, and (c) maximum power output if the turbine were to remain adiabatic.

What is the exit state in this case?

CL.5 A system containing 1 kg of water substance is compressed from 12 bar, 300C

to 20 bar in a quasi-static isothermal process, while being cooled by the envi-

ronment. Determine (a) useful work done by the system, (b) maximum useful

work, and (c) lost work. What is the cause of the lost work?

CL.6 Just as your thermo prof was passing one of the new buildings (under con-

struction), en-route to the Department to conduct an ME209 quiz, a 100 kg

sack of sand (cp = 1000 kJ/kg K) smashed to the ground near him, just miss-

ing him. The zeroth, first, second, and third thoughts to cross his mind were:

(0) Who threw it from the top of the building? (1) what was the ∆S for the

bag of sand? ∆S of the surroundings? (2) What was the amount of entropy

produced? (3) What was the amount of lost work? Please help the prof by

computing the quantities needed to answer (1), (2) and (3). You may assume

that the height of the building is 30 m. Also, it may be a good idea to as-

sume that the initial and final temperature of the bag was 25C, which was

also the temperature of the environment. Even though frictional heating may

have raised the temperature of sand as it fell and smashed to the ground, heat

transfer to the environment would have cooled it to the ambient temperature.

Cycles

CA.1 A Carnot engine uses 1 kg of air as the working fluid. The temperature lim-

its are 300 K and 900 K, the minimum pressure is 1 bar and the volumetric

compression ratio is 20. Determine (a) efficiency, (b) all state points, (c) work

ratio, (d) work done per cycle, (e) heat supplied per cycle, and (f) mean effec-

tive pressure.

CA.2 Repeat the previous exercise for a (a) Stirling cycle and (b) Ericsson cycle.

Limit the maximum pressure, maximum temperature, and minimum volume

to that in th previous exercise. Assume the regenerator to be an ideal one.

Also determine the heat transfer in the regenerator per cycle.


CA.3 Which is the more effective way to increase the efficiency of a Carnot engine:

(a) to increase the temperature of the hot reservoir, keeping that of the cold

reservoir constant, OR (b) to decrease the temperature of the cold reservoir,

keeping that of the hot reservoir constant? Discuss from the point of view of

engineering.

CA.4 What are the expressions for the work done, heat absorbed, and the efficiency

of the cycles shown? Assume the working fluid to be an ideal gas with constant

specific heats.

3

21

2

1

3

12

3 4

(a) (b)

(c)

p

p

p

V

VV

s = const

CA.5 Undertake a standard analysis of the Brayton cycle. Derive expressions for

the efficiency, work ratio, and specific output in terms of the parameters rp

(pressure ratio) and θ (temperature ratio). Determine the value of rp which

maximises the specific output for a fixed θ. Plot numerical values of η, work

ratio, and wsp/cpT1 against rp for different values of θ, for 3 ≤ rp ≤ 20 and

3 ≤ θ ≤ 5.

CA.6 A heat pump working on a reversed Carnot cycle is used to supply 80 kW of

heat for maintaining the rooms of a building at 20C when the outside temper-

ature is 0C. Determine (a) the COP of the system, (b) power consumed by the

heat pump, and (c) heat absorbed from the atmosphere outside. Determine

the power consumption if direct electric heating is used.

CA.7 Determine the COP of a Joule-cycle refrigerator if the environment is at

300 K, the cold space is at 270 K, and (a) the compression ratio is 4, or (b) the

compression ratio is 7. In either case, determine (c) power consumption in

kW/tonne.


CA.8 An Otto cycle with a compression ratio of 7.8 operates from the suction

condition of 1 bar, 300 K. Find the pressure and temperature at the end of

compression and the standard efficiency. Can you determine the temperature

at the end of expansion? Why?

CA.9 In an Otto cycle with a compression ratio of 7, the suction temperature and

pressure are 300 K and 1 bar. Heat supplied during the constant volume

process is 700 kJ/kg. The air flow rate is 90 kg/hr. Determine (a) power

output, (b) mean effective pressure, and (c) efficiency.

CA.10 Derive an expression for the efficiency of a Diesel cycle in terms of the vol-

umetric compression ratio (rv) and the cut-off ratio (rc).

CA.11 Determine the efficiency of a Diesel cycle having a compression ratio of 18,

if the temperature at the beginning of compression is 300 K and that at the

end of expansion is 1000 K.

CA.12 The inlet state in a dual combustion cycle is 1 bar and 300 K. Its compression

ratio is 10. The maximum pressure and temperature in the cycle are 45 bar

and 1800 K. Determine the cycle efficiency.

CA.13 The inlet of a dual combustion cycle is 1 bar and 300 K. Its compression

ratio is 8 and expansion ratio is 5.3. If the isobaric heat absorbed is twice the

isochoric heat absorbed, determine (a) cycle efficiency and (b) MEP.

CA.14 The inlet conditions for an Otto cycle are 1 bar, 290 K. The pressures at

beginning and end of combustion are 15 bar and 40 bar respectively. Determine

(a) compression ratio, (b) standard efficiency, and (c) MEP. If the relative

efficiency of an engine using this cycle is 50%, and the calorific value of the fuel

burnt is 42 MJ/kg, determine (d) efficiency, and (e) specific fuel consumption.

CA.15 The fuel cut-off in a Diesel cycle takes place at 5% of the stroke. If the

compression ratio is 20, determine the standard efficiency.

CA.16 Consider a Brayton cycle with reheat. Let rp and θ be the pressure ratio for

the compressor and the temperature ratio for the cycle, respectively. Let rp1

and rp2 be the pressure ratios of the two turbines. Determine the values of rp1

and rp2 that maximise the specific output. For such an optimal-reheat cycle,

what is the ‘best’ value of rp for fixed θ?

CA.17 Calculate the specific output and thermal efficiency of the following ideal

gas turbine plants.

(a) Basic plant: rp = 8, compressor inlet at 300 K, turbine inlet at 1200 K.


(b) Reheat plant: Equal pressure ratio for each turbine and the same inlet

temperature for each turbine. Other details as in (a).

(c) Intercooled plant: Equal pressure ratio for each compressor and the same

inlet temperature for each compressor. Other details as in (a).

(d) Regenerative plant: With an ideal regenerator. Other details as in (a).

(e) A plant with reheat, intercooling, and regeneration, as specified in (a)–(d).

(f) Compare and comment on the performance of the cycles from (a) to (e).

CA.18 Rework the previous exercise with compressor efficiency of 0.80 and turbine

efficiency of 0.90.

CA.19 A jet engine working on a clipped, standard Brayton cycle has compressor

inlet state of 1 bar 300 K and turbine inlet state of 6 bar, 1500 K. The turbine

produces just the right amount of power to drive the compressor. The turbine

exhaust is expanded through a nozzle to a pressure of 1 bar. The nozzle exit

area is 1 m2. Determine (a) compressor exit temperature, (b) turbine exit

temperature, (c) turbine exit pressure, (d) nozzle exit velocity, (e) mass flow

rate of the working fluid, (f) power output of the turbine, and (g) static thrust.

CA.20 Consider a Rankine cycle with saturated steam. Undertake a study of such

a plant with steam entering the turbine is dry and saturated at (a) 10 bar,

(b) 30 bar, (c) 50 bar, (d) 70 bar, and (e) 90 bar. In each case, compute

efficiency, steam rate, and dryness fraction of steam at the exit of turbine.

Compare and comment. Assume that the condenser is at 0.06 bar in all cases.

CA.21 Consider a superheated steam plant working at 130 bar, with the condenser

at 0.06 bar. Study the effect of superheating by determination of performance

at 350 ( 50 ) 600C.

CA.22 A water heater system is used to provide heat input to a low-temperature

Rankine cycle with ammonia as the working fluid. Ammonia is superheated

to 90C at 19.62 bar and is condensed at 30C after an isentropic expansion.

The properties of ammonia are as follows:

T p hf hg sf sg vfC bar kJ/kg kJ/kg kJ/kg K kJ/kg K m3/kg

30 11.6 323.16 1468.45 1.2035 4.9820 0.00168

The properties of superheated ammonia are:


p T h s v

bar C kJ/kg kJ/kg K m3/kg

11.66 50 1529 5.1760 122.46

19.62 90 1607 5.1760 81.03

(a) Determine the efficiency of the cycle. (b) If an ideal heat exchanger is used

to recover the superheat of the exhause ammonia, what will be the efficiency?

CA.23 A Rankine cycle plant using steam has the following parameters: boiler exit:

45 bar, 450C; condensation temperature: 30C. Determine: (a) heat absorbed,

(b) heat rejected, (c) specific output, and (d) efficiency. If the turbine has an

isentropic efficiency of 0.9, determine (e) specific output, and (f) efficiency.

CA.24 A steam plant works on the Rankine cycle with reheat. Steam enters the

turbine at 35 bar, 350C, and expands to 8 bar, where it passes through a

reheater, emerging at 350C. It then expands to the condenser temperature

of 40C. For the ideal cycle, compute (a) work done in HP and LP turbines,

(b) heat added in the boiler, (c) heat added in the reheater, (d) pump work,

and (e) efficiency.

CA.25 In an ideal regenerative cycle, steam is generated at 45 bar, 450C. It then

expands to 4 bar, where a fraction of the steam is extracted for feedwater

heating. Condensation is at 30C. Determine (a) fraction of steam extracted,

(b) specific output, (c) total pump work, (d) enthalpy of feedwater entering the

boiler, and (e) efficiency. (f) Compare (b)–(e) with those for a cycle without

regeneration, and comment on the differences.

CA.26 In a nuclear plant, dry saturated steam is supplied to the turbine. The boiler

is at 45 bar, and the condenser at 0.06 bar. During expansion, the steam is

removed thrice from the turbine, the water separated in separators, and dry

saturated steam fed back into the turbine. The pressures at which wet steam

is taken to the separators are 20 bar, 5 bar, and 1 bar. The water separated

in each separator is discharged into the condenser. Determine the state lines

through the turbine, the steam rate, and the efficiency of the plant, if (a) the

turbine and separators are ideal, and (b) the turbine has an efficiency of 0.8 and

the separators have pressure drops of 1.0 bar, 0.5 bar, and 0.2 bar, respectively.

CA.27 A power plant is to be designed to operate on a regenerative cycle with

two contact heaters to heat the feed water to 198.3C. The steam parameters

are 60 bar, 400C and 0.05 bar. If the plant produces 50 MW at generator

terminals, determine the efficiency of the plant. Compare it with the efficiency

of a plant without feed heating. You may assume equal heating in the two

heaters.


CA.28 A Joule-cycle refrigerator works with the environment at 300 K, the cold

system at 250 K, and a compression ratio of 6. The working fluid is air (assume

ideal gas behaviour). For the ideal cycle, determine (a) COP, (b) specific

refrigeration effect, and (c) power supply for a 12-tonne plant. (d) If the

compressor and turbine efficiencies are 90% and 80%, what will be the answers?

CA.29 If, in the previous problem (with compressor and turbine efficiencies as in (d),

an ideal regenerator is used, determine the pressure ratio one can work with,

assuming that the compressor exit temperature is fixed at 400 K. (a) What are

the answers now? (b) If the regenerator is not ideal, how will you account for

its effectiveness? (c) Comculate the answers when the regnerator effectiveness

is 0.90. (d) What is the minimum value of the regenerator effectiveness below

which the refrigerator will not work?

CA.30 A vapour compression cycle with ammonia has −10C as the evaporation

temperature and +35C as the condensation temperature. Assume that the

compressor inlet state is dry saturated vapour and the condenser exit state is

saturated liquid. Determine (a) all state points, (b) COP, (c) power consump-

tion in kW/tonne. (d) Repeat the calculations for a low-temperature cycle

with evaporator and condenser temperatures as −20C and +40C.

CA.31 Repeat the previous exercise with R-134a as the working fluid. Compare the

results and comment.

CA.32 Repeat the preceding two exercises with a compressor isentropic efficiency

of 80%.

CA.33 For air-conditioners, a common refrigerant is R22. Determine the COP

of a vapour compression cycle with R22 that has evaporation at +10C, and

condensation at +40C. Assume that the compressor inlet state is dry saturated

vapour and the condenser exit state is saturated liquid. Determine (a) all state

points, (b) COP, and (c) power consumption in kW/tonne. Study the effect

of compressor efficiency, by considering isentropic efficiencies of 1.0 and 0.8.

Exercises on Psychrometry, Combustion, and Compressible Flow will be provided

separately.

Thermodynamics

Documents

isothermal

engineering

additional

constant specic

volumetric

dry saturated

specic gibbs

dual combustion