Welcome to my Class (trial- II) Physics Ph 1101

Md. Kamrul Hasan Reza Department of Physics

Khulna University of Engineering & Technology

Khulna-9203, Bangladesh

Tel.: +880-41-769468~75 Ext. 587(O), 588 (R)

e-mail: [email protected], [email protected]

Website : www.kuet.ac.bd/phy/reza/

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Welcome to my Class (trial-II)

Physics Ph 1101

11:40 AM

July 22, 2020

COVID-19 Precautions

Don’t be afraid

Be aware of the pandemic

Use appropriate outfits if you

compelled to go out

Try to maintain proper diet

Do not forget to exercise

(at least one hour) regularly

Try to follow the guidelines of WHO and Bangladesh Government

Try to stay at home

Applications of First Law of Thermodynamics Specific Heat of a Gas (T and V Independent)

If V and T are chosen as the independent variables

U = f (V, T) ….(1)

Differentiating eq. (1)

….(2)

If an amount of heat δH is supplied to a thermodynamical

system, say an ideal gas and if the volume increases by dV at a

Constant pressure P,

Then according to the first law of thermodynamics

δH = dU + δW

Here δW = P . dV

∴ δH = dU + PdV

Substituting the value of dU from eq. (2)

….(3)

Dividing both sides of eq. (3) by dT

….(4)

If the gas is heated at constant volume

….(5)

When the gas is heated at constant pressure

∴ From eq. (4)

….(6)

From Joule's experiment, for an ideal gas on opening the stop-

cock, no work was done and no heat transfer took place.

So, δH = 0 = dU + 0. Therefore, dU = 0. Even though the

volume changed while the temperature is constant, there is no

change in internal energy.

References: Heat and Thermodynamics – Brij Lal & N. Subrahmanyam

and materials from internet resources

From the ideal gas equation

PV = RT

….(7)

….(8)

Here CP, CV and R are expressed in the same units.

From eq. (3)

….(9)

For a process at constant temperature

dT = 0

….(10)

This equation represents the amount of heat energy supplied

to a system in an isothermal reversible process and is equal to

the sum of the work done by the system and the increase in its

internal energy.

For a reversible adiabatic process

δH = 0

Therefore from eq. (9)

Dividing throughout by dV

….(11)

….(12)

The isobaric volume coefficient of expansion

….(13)

….(14)

From eq. (12) and (14)

….(15)

This expression holds good for an adiabatic reversible Process.

Slopes of Adiabatics and Isothermals In an isothermal process

PV = Constant

Differentiating eq. (15)

P dV + V dP = 0

….(15)

….(16)

Fig. 1: P-V diagram to show the slopes of adiabats and isotherms

In an adiabatic process

P Vϒ = Constant ….(17)

Differentiating eq. (17)

P ϒ Vϒ-1 dV + V dP = 0

….(18)

Therefore, the slope of an adiabatic is ϒ times the slope of the

isothermal.

Work Done During an Isothermal Process

….(19)

Considering one gram molecule of the gas

P V = R T

Fig. 2: P-V diagram of an isotherm

….(20)

Also P1 V1 = P2 V2

….(21)

Here, the change in the internal energy of the system is zero

(temperature constant). So the heat transferred is equal to

the work done

Work Done During an Adiabatic Process

….(22)

Fig. 3: P-V diagram of an adiabat

During an adiabatic process

P Vϒ = Constant = K

….(23)

Since A and B lie on the same adiabatic

Taking TA and TB as the temperatures at the points A and B

respectively and considering one gram molecule of the gas

P1V1 = R T1

and P2 V2 = R T2

Substituting these values in eq. (24)

….(24)

….(25)

Here, heat transferred is zero because the system is thermally

insulated from the surroundings. The decrease in the internal

energy of the system (due to fall in temperature) is equal to

the work done by the system and vice versa.

Relation Between Adiabatic and Isothermal Elasticities

During an isothermal process

PV = Constant

Differentiating eq.(26)

P dV + V dP = 0

….(26)

….(27)

Isothermal Elasticity

From the definition of elasticity of a gas

….(28)

From eq. (27) and (28)

….(29)

Adiabatic Elasticity

During an adiabatic process

PVϒ = Constant ….(30)

Differentiating eq. (30)

P ϒ Vϒ-1 dV + Vϒ dP = 0

….(31)

From the definition of elasticity of a gas

….(32)

From eq. (31) and (32)

Eadi = ϒP ….(33)

Comparing eqs. (29) and (33)

….(34)

Thus, the adiabatic elasticity of a gas is ϒ times the isothermal

elasticity

Irreversible Process

The thermodynamical state of a system can be defined with

the help of the thermodynamical coordinates of the system.

The state of a system can be changed by altering the

thermodynamical coordinates. Changing from one state to

the other by changing the thermodynamical coordinates is

called a process.

Consider two states of a system ie., state A and state B.

Change of state from A to B or vice versa is a process and the

direction of the process will depend upon a new

thermodynamical coordinate called entropy.

Consider the following processes :

Let two blocks A and B at different temperatures T1 and T2

(T1>T2) be kept in contact but the system as a whole is insulated

from the surroundings. Conduction of heat takes place between

the blocks, the temperature of A falls and the temperature of B

rises and thermodynamical equilibrium will be reached.

Consider two flasks A and B connected by a glass tube provided

with a stop cock. Let A contain air at high pressure and B is

evacuated. The system is isolated from the surroundings. If the

stop cock is opened, air rushes from A to B, the pressure in A

decreases and the volume of air increases.

processes in which the entropy of an isolated system

decreases do not take place or for all processes taking place

in an isolated system the entropy of the system should

increase or remain constant

Reversible Process

A reversible processes is one in which an infinitesimally small

change in the external conditions will result in all the changes

taking place in the direct process but exactly repeated in the

reverse order and in the opposite sense.

Second Lew of Thermodynamics

Kelvin-Planck statement of the second law is as follows:

It is impossible to get a continuous supply of work from a

body (or engine) which can transfer heat with a single heat

reservoir.

According to Kelvin, it is impossible to get a continuous

supply of work from a body, by cooling it to a temperature

lower than that of its surroundings.

According to Clausius, it is impossible to make heat flow from a

body at a lower temperature to a body at a higher temperature

without doing external work on the working substance.