Engineering Thermodynamics (2131905) B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1.1 CHAPTER 1 – BASIC CONCEPTS THEORY 1. Explain briefly the following terms with diagram (wherever necessary): a) Thermodynamic System, Surroundings & Boundary b) Control Volume & Control Surface c) Intensive & Extensive Property d) Path Function & Point Function e) Thermodynamic Equilibrium 2. Differentiate open system and control volume. Explain types of system with appropriate examples. 3. Discuss microscopic and macroscopic point of view in thermodynamics. OR How classical thermodynamics does differs from statistical thermodynamics. 4. Explain quasi static process with necessary diagrams.
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CHAPTER 1 BASIC CONCEPTS · [Ans: 458.8 kW] [3.35, R.K.Rajput] ... 0.2 m3 of an ideal gas at a pressure of 2 MPa and 600K is expanded isothermally to 5 times the initial volume. It
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Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1.1
CHAPTER 1 – BASIC CONCEPTS
THEORY
1. Explain briefly the following terms with diagram (wherever necessary):
a) Thermodynamic System, Surroundings & Boundary
b) Control Volume & Control Surface
c) Intensive & Extensive Property
d) Path Function & Point Function
e) Thermodynamic Equilibrium
2. Differentiate open system and control volume. Explain types of system with
appropriate examples.
3. Discuss microscopic and macroscopic point of view in thermodynamics.
OR
How classical thermodynamics does differs from statistical thermodynamics.
4. Explain quasi static process with necessary diagrams.
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2.1
CHAPTER 2 – FIRST LAW OF THERMODYNAMICS
THEORY
1. State 1st Law of thermodynamics. Write down expressions for the first law applied to
(i) a cycle and (ii) a process. What is difference between heat and work? Explain the
conventional meanings for positive-ness and negative-ness for heat and work
interactions between thermodynamic system and its surroundings across the
system boundary.
2. State the first law of thermodynamics, its applications and limitations.
3. Define “Internal Energy” and prove that it is a property of the system. OR Prove that
‘Energy’ is a point function of a system undergoing change of state.
4. Write continuity equation. Derive the general steady flow energy equation. Making
suitable assumptions reduce the same for different engineering applications (i.e.
Nozzle, Boiler, Cooling Tower, Steam or Gas Turbine, Hydraulic Turbine,
Reciprocating Compressor, Rotary Compressor, Centrifugal Water Pump, Expansion
Valve of Refrigerator, etc.)
5. Derive equation for (a) filling of a tank and (b) emptying of tank.
6. Explain displacement work and flow work.
CLASS TUTORIAL
1. At the inlet to a certain nozzle the enthalpy of fluid passing is 2800 kJ/kg, and the
velocity is 50 m/s. At the discharge end the enthalpy is 2600 kJ/kg. The nozzle is
horizontal and there is negligible heat loss from it.
a. Find the velocity at exit of the nozzle.
b. If the inlet area is 900 cm2 and the specific volume at inlet is 0.187 m3/kg,
find the mass flow rate.
c. If the specific volume at the nozzle exit is 0.498 m3/kg, find the exit area of
nozzle. [Ans: 634.4 m/s, 24.06 kg/s, 188.87 cm2] [3.42, R. K. Rajput]
2. In a gas turbine unit, the gases flow through the turbine is 15 kg/s and the power
developed by the turbine is 12000 kW. The enthalpies of gases at the inlet and outlet
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2.2
are 1260 kJ/kg and 400 kJ/kg respectively, and the velocity of gases at the inlet and
outlet are 50 m/s and 110 m/s respectively. Calculate:
a. The rate at which heat is rejected to the turbine, and
b. The area of the inlet pipe given that the specific volume of the gases at the
inlet is 0.45 m3/kg. [Ans: 828 kW, 0.135 m2] [3.33, R. K. Rajput]
3. In an air compressor air flows steadily at the rate of 0.5 kg/s through an air
compressor. It enters the compressor at 6 m/s with a pressure of 1 bar and a specific
volume of 0.85 m3/kg and leaves at 5 m/s with a pressure of 7 bar and a specific
volume of 0.16 m3/kg. The internal energy of the air leaving is 90 kJ/kg greater than
that of the air entering. Cooling water in a jacket surrounding the cylinder absorbs
heat from the air at the rate of 60 kJ/s. Calculate:
a. The power required to drive the compressor;
b. The inlet and output pipe cross-sectional area.
[Ans: 118.5 kW, 0.016 m2] [3.34, R. K. Rajput]
4. A centrifugal pump delivers 50 kg of water per second. The inlet and outlet
pressures are 1 bar and 4.2 bar respectively. The suction is 2.2 m below the centre of
the pump and delivery is 8.5 m above the centre of the pump. The suction and
delivery pipe diameters are 20 cm and 10 cm respectively. Determine the capacity of
the electric motor to run the pump. [Ans: 22.2 kW] [3.45, R. K. Rajput]
5. Air at a temperature of 20°C passes through a heat exchanger at a velocity of 40
m/s where its temperature is raised to 820°C. It then enters a turbine with same
velocity of 40 m/s and expands till the temperature falls to 620°C. On leaving the
turbine, the air is taken at a velocity of 55 m/s to a nozzle where it expands until the
temperature has fallen to 510°C. If the air flow rate is 2.5 kg/s, calculate:
a. Rate of heat transfer to the air in the heat exchanger;
b. The power output from the turbine, assuming no heat loss;
c. The velocity at exit from the nozzle, assuming no heat loss
[Ans: 2010 kJ/s, 504.3 kW, 473.4 m/s] [3.47, R. K. Rajput]
6. In a steam plant, 1 kg of water per second is supplied to the boiler. The enthalpy and
velocity of water entering the boiler are 800 kJ/kg and 5 m/s. The water receives
2200 kJ/kg of heat in the boiler at constant pressure. The steam after passing
through the turbine comes out with a velocity of 50 m/s, and its enthalpy is 2520
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2.3
kJ/kg. The inlet is 4 m above the turbine exit. Assuming the heat losses from the
boiler and the turbine to the surroundings are 20kJ/s, calculate the power
developed by the turbine. Consider the boiler and turbine as single system.
[Ans: 458.8 kW] [3.35, R.K.Rajput]
ASSIGNMENT
PART 1 – NON FLOW PROCESSES
1. A domestic refrigerator is loaded with food and the door closed. During a certain
period the machine consumes 1 kW h of energy and the internal energy of the
system drops by 5000 kJ. Find the net heat transfer for the system.
[Ans: -8.6MJ] [GTU – JAN 2017]
2. A cylinder contains 0.45 m3 of gas at 1 x 105 N/m2 and 80°C. The gas is compressed
to a volume of 0.13m3. The final pressure being 5 x 105 N/m2. Assume γ=1.4,
R=294.2 J/Kg°C. Calculate mass of gas, index of compression n, increase in internal
energy of gas, heat rejected by gas during compression.
[Ans: 0.433kg, 1.296, 49.9kJ, 17.54kJ] [GTU – OCT 2012]
3. 0.2 m3 of an ideal gas at a pressure of 2 MPa and 600K is expanded isothermally to 5
times the initial volume. It is then cooled to 300K at constant volume and then
compressed back polytropically to its initial state. Determine the net work done and
heat transfer during the cycle. [Ans: 181.88kJ, 0]
4. Calculate the final temperature, pressure, work done and heat transfer if the fluid is
compressed reversibly from volume of 6m3 to 1 m3 when the initial temperature and
pressure of fluid as 20°C and 1 bar respectively. Assume the index of compression as
1.4, Cp = 1.005 and Cv = 0.718 and R = 0.287 KJ/kg-K.
[GTU – DEC 2014][Ans: 599.968K, 12.286bar, -1.5715MJ, 0]
Part 2 – Steady Flow Energy Equation
5. A nozzle is a device for increasing the velocity of a steadily flowing stream. At inlet
to a certain nozzle, the fluid parameter are Enthalpy = 2850 kJ/kg, velocity = 50 m/s,
area = 0.1 m2, specific volume = 0.18 m3/kg at the discharge end enthalpy is 2650
kJ/kg and the specific volume is 0.49 m3/kg. Make calculation for the velocity of fluid
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2.4
at exit from the nozzle, mass flow rate of fluid and the exit area of the nozzle. The
nozzle is horizontal and there is negligible heat loss from it.
11. Steam at 6.87bar, 205°C enters in an insulated nozzle with a velocity of 50m/sec. It
leaves at a pressure of 1.37bar and a velocity of 500m/sec. Determine the final
enthalpy of the steam. Also clearly mentioned the applied assumptions. Use of
steam table is permitted.
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3.1
CHAPTER – 3 SECOND LAW OF THERMODYNAMICS
THEORY
1. Define below terms:
a) Heat Engine
b) Thermal Energy Reservoir
c) Refrigerator
d) Heat Pump
2. Give Kelvin-Plank and Clausius statement of 2nd law of thermodynamics and prove
their equivalency. OR
Prove that violation of Kelvin-Plank statement leads to violation of Clausius
statement and violation of Clausius statement leads to violation of Kelvin-Plank
statement.
3. Prove that all reversible engines operating between operating between same
temperatures limits have are equally efficient.
4. Explain Carnot theorem. OR
State and prove Carnot’s theorem for Heat Engine and also write statement of
Carnot’s theorem in the view of refrigerator and Heat Pump
5. Justify that Carnot cycle is impracticable. OR
Identify the reasons for the impracticability of Carnot cycle.
6. State and explain the Perpetual motion machines of Second Kind.
7. State the comparisons of First law and Second law of thermodynamics.
8. Derive an expression for Carnot efficiency with usual notations.
9. Explain thermodynamics temperature scale.
CLASS TUTORIAL
1. Two Carnot engines work in series between the sources and sink temperatures of
550K and 350K. If both engines develop equal power, derive the formulae to find out
the intermediate temperature and determine the intermediate temperature also. 2. A heat engine produces a work equivalent to 80 kW with an efficiency of 40%.
Determine the heat transfer rate to and from the working fluid.
3. A heat engine develop 10 kW power when receiving heat at the rate of 2250
kj/min. Evaluate the corresponding rate of heat rejection from the engine and its
thermal efficiency.
4. A machine operating as a heat pump extracts heat from the surrounding
atmosphere is driven by a 7.5 kW motor and supplies heat to a
house needed for its heating in winter. Find coefficient of performance for heat
pump. How this COP will be affected if the objection of the same machine is to
cool house in summer requiring of heat rejection? Comment on
result.
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3.2
5. A reversed Carnot cycle operates at either a refrigerator or heat pump. In either
case, the power input is 20.8 kW. Calculate the quantity of heat extracted from
the cold body for either type of machine. In both case 3500 kJ/min heat is
delivered by the machine. In case of the refrigerator the heat is transferred to the
surroundings while in case of heat pump, the space is to be heated. What is their
respective coefficient of performances? If the temperature of cold body is 0°C for
the refrigerator and 5°C for heat pump what will be respective temperatures of
surrounding for refrigerator and heated space for heat pump? What reduction in
heat rejection temperatures would be achieved by doubling the COP for same
cold body temperature?
6. A Carnot engine receives 5000 KJ as heat from a heat source at 4270C and rejects
to atmosphere at 270C. Calculate the thermal efficiency of engine and work
produced by engine. If engine is irreversible and efficiency of this irreversible
engine is 75% of Carnot engine, find the percentage change in heat rejection for
the same heat input and temperature limit.
7. An engine manufacturer claims to have developed a heat engine with following
specifications:
Power developed = 75 kW
Fuel burnt = 5 kg/hr
Heating value of fuel = 75000 kJ/kg
Temperature limits = 1000 K and 400 K
Is the claim of an engine manufacturer true or false? Provide your explanation.
8. A reversible engine receives heat from two thermal reservoirs maintained at
constant temperature of 750 K and 500 K. The engine develops 100 kW and
rejects 3600 kJ/min of heat to a heat sink at 250 K. Determine thermal efficiency
of the engine and heat supplied by each thermal reservoir.
ASSIGNMENT
1. A refrigerator operating on reversed Carnot cycle whose C.O.P is 5. The
evaporator is maintained at a temperature of -6⁰C and the power required to run
the refrigerator is 3.5 kW. Determine the refrigerating effect and the condenser
temperature of the refrigerator. [Answer: (1) R.E (Q2) = 17.5 kW; (2) T1 = 320.4 K] D.S. Kumar 203/7.9
2. Which is more effective way to increase the efficiency of a Carnot heat engine:
Case-(i) to increase the source temperature T1 while the sink temperature T2 is
held constant or Case-(ii) to decrease the sink temperature by the same amount
while the source temperature is held constant? How this result would be affected
in case of a Carnot heat pump? [Answer: for heat engine: Case- (ii) is more
effective, for heat pump: Case- (i) is more effective]
D. S. Kumar 206/7.16
Engineering Thermodynamics (2131905)
B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3.3
3. An inventor claims that his engine has the following specifications: Source temperature = 450 K
Sink temperature = 280 K
Power delivered = 0.15 kWh
Heat supplied = 1200 kJ
As a patent officer, would you issues a patent for such an engine? Give your
clarification.
[Answer: Claim is false; the patent is not to be issued] D.S. Kumar 211/7.19
4. An inventor claims that his engine absorbs 300 kJ of energy from a thermal
reservoir at 325 K and delivers 75 kJ of work. The inventor also states that his
engine has two heat rejections: 125 kJ to a reservoir at 300 K and 100 kJ to a
reservoir at 275 K. Check the validity of his claim.
[Answer: Claim of inventor is intolerable] D.S. Kumar 217/7.22
5. A reversible engine is supplied 900 kJ of heat from a heat source at 500 K. The
engine develops 300 kJ of net work and rejects heat to two heat sinks at 400 K
and 300 K. Determine thermal efficiency and magnitude of heat interaction with
each of the sink.
[Answer: (1) η = 33.3%; (2) Heat rejected to sink at 400 K = 240 kJ, heat rejected
at 300 K = 360 kJ] D.S. Kumar 220/7.26
6. A heat engine work between hot and cold reservoir at 600 K and 300 K. The
engine receives 300 kW of heat. Identify which of the following heat rejections
represents reversible, irreversible and impossible cycle: