The pressure P1 and density d1 of diatomic gas (γ=(7/5)) changes suddenly to P 2( P 1) and d 2 respectively during an adiabatic process. The temperature of the gas increases and becomes times of its initial temperature. (given ( d 2/ d 1)=32 )

Question

The pressure P1 and density d1 of diatomic gas (&gamma;=(7/5)) changes suddenly to P 2(> P 1) and d 2 respectively during an adiabatic process. The temperature of the gas increases and becomes times of its initial temperature. (given ( d 2/ d 1)=32 ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

PV &gamma;= text const d =( m / V ) p (( m / d ))&gamma;= text const ( p / d &gamma;)= text const ( p 1/ p 2)=(( d 1/ d 2))&gamma;=((1/32))7 / 5=(1/128) ( T 1/ T 1)=( P 1 V 1/ P 2 V 2)=(1/128) 32=(1/4)

Q. The pressure $P_{1}$ and density $d_{1}$ of diatomic gas $(γ = \frac{7}{5})$ changes suddenly to $P_{2} (> P_{1})$ and $d_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes ___ times of its initial temperature.
(given $\frac{d _{2}}{d _{1}} = 32$ )

$P V^{γ} = const d = \frac{m}{V}$
$p (\frac{m}{d})^{γ} = const$
$\frac{p}{d ^{γ}} = const$
$\frac{p _{1}}{p _{2}} = (\frac{d _{1}}{d _{2}})^{γ} = (\frac{1}{32})^{7/5} = \frac{1}{128}$
$\frac{T _{1}}{T _{1}} = \frac{P _{1} V _{1}}{P _{2} V _{2}} = \frac{1}{128} 32 = \frac{1}{4}$

Q. The pressure P1​ and density d1​ of diatomic gas (γ=57​) changes suddenly to P2​(>P1​) and d2​ respectively during an adiabatic process. The temperature of the gas increases and becomes ___ times of its initial temperature. (given d1​d2​​=32 )

PVγ= const d=Vm​ p(dm​)γ= const dγp​= const p2​p1​​=(d2​d1​​)γ=(321​)7/5=1281​ T1​T1​​=P2​V2​P1​V1​​=1281​32=41​

Q. The pressure $P_{1}$ and density $d_{1}$ of diatomic gas $(γ = \frac{7}{5})$ changes suddenly to $P_{2} (> P_{1})$ and $d_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes ___ times of its initial temperature.
(given $\frac{d _{2}}{d _{1}} = 32$ )

$P V^{γ} = const d = \frac{m}{V}$
$p (\frac{m}{d})^{γ} = const$
$\frac{p}{d ^{γ}} = const$
$\frac{p _{1}}{p _{2}} = (\frac{d _{1}}{d _{2}})^{γ} = (\frac{1}{32})^{7/5} = \frac{1}{128}$
$\frac{T _{1}}{T _{1}} = \frac{P _{1} V _{1}}{P _{2} V _{2}} = \frac{1}{128} 32 = \frac{1}{4}$