Question

Two moles of an ideal monoatomic gas at $27^{\circ }C$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2V$, then the work done by the gas will be $\left(\gamma =\frac{5}{3},R=8.31J/molK\right)$

• A. +2767.23 J
• B. 2627.23 J
• C. 2500 J
• D. -2500 J

Answer 1

Answer: (A)

As, $W=\frac{\mu R\left(T_1-T_2\right)}{(\gamma -1)}$
$=\frac{\mu R{T}_1}{(\gamma -1)}\left[1-\frac{T_2}{T_1}\right]$
$=\frac{\mu R{T}_1}{(\gamma -1)}\left[1-{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}\right]$
$=\frac{2\times 8.31\times 300}{\left(\frac{5}{3}-1\right)}\left[1-{\left(\frac{1}{2}\right)}^{\frac{5}{3}-1}\right]$
$=+2767.23J$