Question

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy -

• A. (a) 189 K (b) 2.7 kJ
• B. (a) 195 K (b) - 2.7 kJ
• C. (a) 189 K (b) -2.7 kJ
• D. (a) 195 K (b) 2.7 kJ

Answer 1

Answer: (C)

(a) 189 K (b) -2.7 kJ

Answer 2

$T V^{\gamma-1}=$ Constant $T_{f}=300\left(\frac{V}{2 V}\right)^{\frac{5}{3}-1}=189\,, K$ $\Delta U=n C_{v} \Delta T=2 \times \frac{3 R}{2} \times[189-300]$ $=-2.7 \,kJ$