## Book: HC Verma - Concepts of Physics Part 2

### Chapter: 27. Specific Heat Capacities of Gases

#### Subject: Physics - Class 12th

##### Q. No. 10 of Exercises

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

10
##### An ideal gas (CP/CV = γ) is taken through a process in which the pressure and the volume vary as p = αVb. Find the value of b for which the specific heat capacity in the process is zero.

Given:

p = aVb

p = pressure, V = volume, a and b are constants.

Formula used:

We know, Q = U + pdV from first law of thermodynamics,

where Q = change in heat, U = change in internal energy and pdV = W = total work done, p = pressure, V = volume.

Since Q = nCdT, and U = nCvdT, we get

… (ii), n = no. of moles, C = specific

heat capacity, and Cv = specific heat capacity at constant volume,

dT = change in temperature,

Since specific heat capacity is 0(given),

…(iii)

(after integration of from V1 to V2)

Now, from equation of state, PV = nRT,

Where

P = pressure,

V = volume,

n = number of moles,

R = universal gas constant,

T = temperature.

Substituting p = aVb from (i):

aVb+1 = nRT

=> … (iv)

Substituting (iv) in (iii),

(Since (T2 - T1) = dT)

=>

=> b = -

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35