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

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

#### Subject: Physics - Class 12th

##### Q. No. 4 of Exercises

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4
##### The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g−1 °C−1 and 3.4 cal g−1 °C−1 respectively. The molecular weight of hydrogen is 2 g mol−1 and the gas constant, R = 8.3 × 107 erg °C−1mol−1. Calculate the value of J

Given:

Specific heat at constant volume is Cv =2.4 cal g-1oC-1

Specific heat at constant pressure is Cp=3.4 cal g-1oC-1

Molecular mass of hydrogen is 2 g mol-1

Gas constant, R=8.3× 107 gmol

Formula used:

Where:

m is the molecular weight of hydrogen

Cp is the specific heat at constant pressure

Cv is the specific heat at constant volume

R is the gas constant.

Putting the values in the above equation , we get

The gas constant R= (m X Cp ) - (m X Cv) = 2 × (Cp-Cv)= 2×J

Now, 2× J=R

2× J=8.3 × 107 erg/ mol-oC

Thus, J=4.15 × 107 erg/cal (Answer).

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