C_p and C_v are the specific heats at constant pressure and constant volume respectively. It is observed that C_p - C_v = a for hydrogen gas and C_p - C_v = b for carbon dioxide gas. The correct relationship between ' a' and 'b' is ( atomic weight of hydrogen , carbon and oxygen are 1u, 12 u and 16 u respectively)

Step-by-step solution

For a given gas, the molar heat capacities at constant pressure and constant volume are related by Mayer's relation: C_ P,m - C_ V,m = R The specific heat is defined as the heat capacity per unit mass. Therefore, the difference between the specific heats at constant pressure ( C_p ) and constant volume ( C_v ) is given by: C_p - C_v = R M where M is the molar mass of the gas. For hydrogen gas ( H₂ ), the molar mass is M_ H₂ = 2 1 = 2 u. Thus: a = R 2 For carbon dioxide gas ( CO₂ ), the molar mass is M_ CO₂ = 12 + 2