Question

A monoatomic ideal gas initially at $17{}^{\circ }C$ is suddenly compressed to one eighth of its original volume. The temperature after compression is:

• A. $17{}^{\circ }C$
• B. $887{}^{\circ }C$
• C. $16{}^{\circ }C$
• D. none of these

Answer 1

Answer: (B)

From the formula $T{V}^{\gamma -1}=\text{constant}$ $\left[Here:V_2=\frac{V_1}{8},\gamma =\frac{5}{3}\right]$ Hence, $T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$ $\frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}={\left(\frac{1}{1/8}\right)}^{5/3-1}$ $T_2={(8)}^{2/3}\times T_1$ $=4\times 290=1160K=887{}^{\circ }C$