Verified 30 May 2026.
Two moles of an ideal monoatomic gas occupy a volume $2V$ at temperature $300\,\text{K}$. The gas expands adiabatically to a volume $16V$. The temperature of the gas after expansion is approximately:
$150\,\text{K}$
$75\,\text{K}$
$100\,\text{K}$
$120\,\text{K}$
For adiabatic process: $TV^{\gamma-1} = \text{const}$
For monoatomic gas, $\gamma = \frac{5}{3}$, so $TV^{2/3} = \text{const}$
$$300 \cdot (2V)^{2/3} = T_2 \cdot (16V)^{2/3}$$
$$T_2 = 300 \cdot \left(\frac{2}{16}\right)^{2/3} = 300 \cdot \left(\frac{1}{8}\right)^{2/3} = 300 \cdot \frac{1}{4} = 75\,\text{K}$$
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