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HEAT AND THERMODYNAMICS

1. Expansion of solids :

a) Coefficient of linear expansion :0

L

L t

=

b) Coefficient of superficial expansion :0

A

A t

=

c) Coefficient of volume expansion :0

VV t =

d) 2 ; 3

2. Density of material at any temperature : 0t(1 t)

=

+

3. Expansion of liquids : If a and g are the apparent coefficient of expansion of liquid and volume

coefficient of expansion of container, then t 0r a g a0

V V

V t

= + = .

4. Expansion of gases : v1

/ C273

= , p1

/ C273

= .

5. Law of mixture : Heat lost = heat gained.

6. First law of thermodynamics : H U W = + .

Here H = heat supplied to the system, U = change in internal energy, W = work done by gas.

Some important points :

Work is path dependent in thermodynamics.

Work is taken as positive when system expands against external force.

W PdV= The area of P-V diagram gives work done.

In cyclic process, work done is area of P-V diagram cycle. It is positive when process is clockwise.

It is negative when process is anticlockwise. The change in internal energy is independent of path. It depends only on initial and final states.

For ideal gas

If nPV constant=

P(Pressure)

U(Internal

Energy)

IsobaricIsochoric

Adiabatic

Isothermal

V

Pn=0, (Isobaric)

n=1(Isothermal)

n=2(Adiabatic)n=(Isochoric)

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7. Thermodynamic processes :

S.No. ProcessLaw

applicable

Quantity

remains

constant

U W H U W = +

1. IsochoricGay-

Lussacs lawVolume VnC dT 0 VnC dT

2. Isobaric Charles law Pressure VnC dT P(V2 V1) PnC dT

3.Free

expansion

Temperature 0 0 0

4.Isothermal

processBoyles law Temperature 0

2

1

VnRTln

V

2

1

VnRTln

V

5.Adiabatic

process

PV constant =W

1 2nR(T T )

1

0

6.Polytropic

process

nPV constant=VnC dT

1 1 2 2P V P V

(n 1)

7.Cyclic

process 0

Area of P-V

diagramW

8. of the mixture 1 2 1 21 2

n n n n1 1 1

+ = +

.

9. Molar heat capacity C is the heat required to raise the temperature of 1 mole of a gas by 1C or 1 K.

QC

n T

=

The most general expression for C in the process xPV = constant is

R RC

1 1 x= +

For isobaric process P = constant or x = 0

VC C R= +

For isothermal process x = 1

C =

For adiabatic process x = r

C = 0.

10. Heat conduction :

dH dKA

dt dx

=

Here,d

dx

= temperature gradient, K = thermal conductivity.

Unit of K is watt per metre per Kelvin.

11. Radiation :

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a) Stefans law : 4H

e TA t

=

Here,H

A t

= rate of radiated energy per unit area

= Stefans constant = 5.67108 Wm2 K4 ; e = emissivity, T = temperature of body in Kelvin

b) Kirchhoffs law :

If a = absorptive power, e0 = emissive power then e/a = emissive power of block body.

12. Weins displacement law :

3mT constant 2.892 10 mK

= =

13. Newtons law of cooling :

0

dK( )

dt

= , Here = temperature of body, 0 = temperature of surroundings.

Previous questions :

1. A real gas behaves like an ideal gas if its

a) pressure and temperature are both high b) pressure and temperature are both low

c) pressure is high and temperature is low d) pressure is low and temperature is high

Sol. (d)

A real gas behaves like an ideal gas at low pressure and high temperature.

2. One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its

pressure at A is P0. Choose the correct option(s) from the following.

a) Internal energies at A and B are the same

b) Work done by the gas in process AB is P0V0 n 4

c) Pressure at C is P0/4

d) Temperature at C is T0/4

Sol. (a, b)

3. Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T1 and T2, respectively.

The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm.

Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to

that of B?

Sol. (9)

4. A piece of ice (heat capacity = 2100 J kg1

C1

and latent heat = 3.36 105 J kg1) of mass m grams isat

5C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the

ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other

heat exchange in the process, the value of m is

Sol. (8)5. A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. If the initial temperature

of the gas is Ti (in Kelvin) and the final temperature is aTi, the value of a is

Sol. (4)

T0

V0C

B

A

T

V

4V0