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Question:

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P_0, volume V_0 and temperature T_0. If the gas mixture is adiabatically compressed to a volume V_0/4, then the correct statement(s) is/are,(Given 2^1.2 = 2.3 ; 2^3.2 = 9.2 ; R is gas constant)

The final pressure of the gas mixture after compression is in between 9P_0 and 10 P_0

Adiabatic constant of the gas mixture is 1.6

The work |W| done during the process is 13 RT_0

The average kinetic energy of the gas mixture after compression is in between 18 RT_0 and 19 RT_0

Solution:

Correct option is D. The work |W| done during the process is 13 RT_0
γ_mix = (n_1 C_P1 + n_2C_P2)/(n_1 C_V1 + n_2C_V2) = 8/5
W = (P_1 V_1^γ - P_2V_2^γ)/(γ - 1)
P_0V_0^(8/5) = P_2 (V_0/4)^(8/5)
P_2 = 9.2 P_0
W = P_0V_0 - 9.2P_0 V_0/4^(3/5) = -13RT_0
∴ |W| = 13 RT_0
(2) T_1 V_1^(γ - 1) = T_2V_2^(γ - 1)
T_2 = T_1 (2)^(6/5) = 2.3 T_0
Avergae kinetic energy of gas mixture = nC_V_mix T_2= 23 RT_0