A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (. given, .γ=(3/2)) :

Question

A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (. given, .&gamma;=(3/2)) : (A) W=T R[√2-2] (B) W=(R/T)[2-√2] (C) W=R T[2-√2] (D) W=(T/R)[√2-2]

Tardigrade Admin · Accepted Answer

T1 V1&gamma;-1=T2 V2&gamma;-1 T V1 / 2=T2(2 V)1 / 2 T2=(T/√2) W=(R(T1-T2)/&gamma;-1)=(R(T-(T/√2))/(1)2)=R T(2-√2)

Q. A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $($ given, $γ = \frac{3}{2})$ :

$W = TR [2 - 2]$

$W = \frac{R}{T} [2 - 2]$

$W = RT [2 - 2]$

$W = \frac{T}{R} [2 - 2]$

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$T V^{1/2} = T_{2} (2 V)^{1/2}$
$T_{2} = \frac{T}{2}$
$W = \frac{R ( T _{1} - T _{2} )}{γ - 1} = \frac{R ( T - \frac{T}{2} )}{\frac{1}{2}} = RT (2 - 2)$

Q. A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is ( given, γ=23​) :

W=TR[2​−2]

W=TR​[2−2​]

W=RT[2−2​]

W=RT​[2​−2]