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

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

#### Subject: Physics - Class 12th

##### Q. No. 5 of Objective I

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##### 70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is

We know that, Q = nCpdT… (i),

Where

Q = heat required to raise the temperature

n = number of moles

Cp = specific heat capacity at constant pressure

dT = rise in temperature.

In this first case,

Amount of heat required(Q) = 70 cal

Number of moles(n) = 2 mol

Rise in temperature(dT) = (35-30)0C = 50C

Hence, from (i), we get Cp = 7 calmol-1 0C-1

Now, we know, Cp - Cv = R,

Where

Cp = specific heat capacity at constant pressure

Cv = specific heat capacity at constant volume

R = universal gas constant = 1.98 calmol-1 0C-1

Therefore, we get Cv = Cp - R = (7-1.98) cal mol-1 0C-1

= 5.02 cal mol-1 0C-1

Now, in the new case, change in temperature dT = 50C as before. Number of moles(n) = 2, and Cv = 5.02 calmol-1 0C-1

Hence, amount of heat required to raise the temperature of the same gas through the same range

dQ = nCvdT = (2 x 5.02 x 5) cal = 50.2 cal which is approximately equal to 50 cal.

Hence, the correct option is (b).

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