Question 1: Thermodynamics & KTG

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 ${{{V_0}} \over 4}$, then the correct statement(s) is/are
(Given, 2
1.2
= 2.3; 2
3.2
= 9.2; R is a gas constant)

Accepted Answer

${\gamma _{mix}} = {{{n_1}{C_{p1}} + {n_2}{C_{p2}}} \over {{n_1}{C_{v1}} + {n_2}{C_{v2}}}} = {8 \over 5}$
$W = {{{P_1}{V_1} - {P_2}{V_2}} \over {\gamma  - 1}}$
${P_0}{V_0}^{8/5} = {P_2}{\left( {{{{V_0}} \over 4}} ight)^{8/5}}$
${P_2} = 9.2{P_0}$
$W = {{{P_0}{V_0} - 9.2{P_0}{{{V_0}} \over 4}} \over {3/5}} =  - 13R{T_0}$
$ 	herefore $ $|W| = 13R{T_0}$
(b) ${T_1}V_1^{\gamma  - 1} = {T_2}V_2^{\gamma  - 1}$
${T_2} = {T_1}{(2)^{6/5}} = 23{T_0}$
Average kinetic energy of gas mixture
= $nC{v_{mix}}{T_2} = 23R{T_0}$

Answer

The final pressure of the gas mixture after compression is in between 9P
0
and 10P
0

Answer

The average kinetic energy of the gas mixture after compression is in between 18RT
0
and 19RT
0

Answer

Adiabatic constant of the gas mixture is 1.6

Answer

The work |W| done during the process is 13RT
0

Thermodynamics & KTG

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