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 × 10^{7} erg °C^{−1}mol^{−1}. Calculate the value of *J*

**Given:**

*Specific heat at constant volume is C _{v} =2.4 cal g^{-1o}C^{-1}*

Specific heat at constant pressure is C_{p}=3.4 cal g^{-1o}C^{-1}

Molecular mass of hydrogen is 2 g mol^{-1}

Gas constant, R=8.3× 10^{7} gmol

**Formula used:**

Where:

m is the molecular weight of hydrogen

C_{p} is the specific heat at constant pressure

C_{v} 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 C_{p} ) - (m X C_{v}) = 2 × (Cp-Cv)= 2×J

Now, 2× J=R

2× J=8.3 × 10^{7} erg/ mol^{-o}C

Thus, J=4.15 × 10^{7} erg/cal (Answer).

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