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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 P0, volume V0 and temperature T0. If the gas mixture is adiabatically compressed to a volume V0/4, then the correct statement(s) is/are,
(Given 21.2=2.3;23.2=9.2;R is gas constant)


A

The final pressure of the gas mixture after compression is in between 9P0 and 10P0

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B

The average kinetic energy of the gas mixture after compression is in between 18RT0 and 19RT0

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C

Adiabatic constant of the gas mixture is 1.6

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D

The work |W| done during the process is 13RT0

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Solution

The correct option is D

The work |W| done during the process is 13RT0


n1=5 moles CV1=3R2

n2=1 mole CV2=5R2

(CV)m=n1CV1+n2CV2n1+n2=5×3R2+1×5R26=5R3

γn=(Cp)m(Cv)m=85
So, option (3) is correct.

P0V8/50=P2(V04)8/5

P2=9.2P0
Option 'A' is also correct.

(2) T1Vγ11=T2Vγ12

T2=T1(2)6/5=2.3T0

Average kinetic energy of gas mixture = nCVmixT2 =23RT0

(4) W=P1V1P2V2γ1

W=P0V09.2P0V043/5=13RT0

|W|=13RT0


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