A work of 146 kJ is performed on the gas, in order to compress one kilomole of gas adiabatically and in this process the temperature of the gas increases by 7 ° C . The gas is ( R = 8 . 3 J mol - 1 K - 1 )

Step-by-step solution

According to first law of thermodynamics Δ Q = Δ U + Δ W For an adiabatic process, Δ Q=0 ∴ 0 = Δ U + Δ W or Δ U = - Δ W or n C V Δ T = - Δ W or C V = - Δ W n Δ T = - - 146 × 10 3 1 × 10 3 × 7 C v = 20 . 8   J   mol - 1   K - 1 For diatomic gas, C V = 5 2 R = 5 2 × 8.3 = 20.8 J mol - 1  K - 1 Hence the gas is diatomic.