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).