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,
(Give $2^{1.2}=2.3 ; 2^{3.2}=9.2 ; R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P _0$ and $10 P _0$
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT _0$ and $19 RT _0$
$(3)$ The work $| W |$ done during the process is $13 RT _0$
$(4)$ Adiabatic constant of the gas mixture is $1.6$
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,
(Give $2^{1.2}=2.3 ; 2^{3.2}=9.2 ; R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P _0$ and $10 P _0$
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT _0$ and $19 RT _0$
$(3)$ The work $| W |$ done during the process is $13 RT _0$
$(4)$ Adiabatic constant of the gas mixture is $1.6$
- [IIT 2019]
- A
$1,2,3$
- B
$1,2,4$
- C
$1,3,4$
- D
$1,4$
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$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
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- [AIIMS 2011]
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