5.6 dm³ of an unknown gas at S.T.P. requires 52.25 J of heat to raise its temperature by 10°C at constant volume. Calculate C_v , C_p an atomicity of the gas. 

22.4 dm³ of a gas at S.T.P. = 1 mol  

∴  5.6 dm³ of the gas at S.T.P. = 1/22.4 × 5.6 = 0.25 mol

Thus, for 10° rise, 0.25 mol of the gas at constant volume require heat = 52.25 J

∴  For 1° rise, 1 mol of the gas at constant volume will require heat = 52.25×(10 × 0.25) J = 20.9 J

∴  C_v = 20.9 J K⁻¹ mol⁻¹

Now, C_p = C_v + R = 20.9 J K⁻¹ mol⁻¹ + 8.314 J K⁻¹ mol⁻¹ = 29.214 J K⁻¹ mol⁻¹

∴  γ = C_p /C_v =29.214/20.9 = 1.4

Hence, the gas is diatomic.