A mixture of ideal gas contains 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P_, volume V_, and temperature T_.If the gas mixture is adiabatically compressed to a volume V_/4 then the correct statement(s) is /are, (Given 2_ú_ = 2.3; 2_ú_ = 9.2; R is gas constant)
A. Adiabatic constant of the gas mixture is 1.6
B. The final pressure of the gas mixture after compression is in between 9P_ and 10P_
C. The work |W| done during the process is 13RT_
D. The average kinetic energy of the gas mixture after compression is in between 18RT_ and 19RT_
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Answer:
mix
=
n
1
C
V1
+n
2
C
V2
n
1
C
P1
+n
2
C
P2
=
5
8
W=
γ−1
P
1
V
1
−P
2
V
2
P
0
V
0
8/5
=P
2
(
4
V
0
)
8/5
P
2
=9.2P
0
W=
3/5
P
0
V
0
−9.2P
0
4
V
0
=−13RT
0
∴∣W∣=13RT
0
(2)T
1
V
1
γ−1
=T
2
V
2
γ−1
T
2
=T
1
(2)
6/5
=2.3T
0
Average kinetic energy of gas mixture = nC
V
mix
T
2
=23RT
0
October 15, 2019
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