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 $2\, V$, then the work done by the gas will be $\left(\gamma=\frac{5}{3}, R=8.31\, J / mol K \right)$

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

Answer 1

Answer: (A)

As, $W=\frac{\mu R\left(T_{1}-T_{2}\right)}{(\gamma-1)}$
$=\frac{\mu R T_{1}}{(\gamma-1)}\left[1-\frac{T_{2}}{T_{1}}\right]$
$=\frac{\mu R T_{1}}{(\gamma-1)}\left[1-\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1}\right]$
$=\frac{2 \times 8.31 \times 300}{\left(\frac{5}{3}-1\right)}\left[1-\left(\frac{1}{2}\right)^{\frac{5}{3}-1}\right]$
$=+2767.23\, J$