1. Tardigrade
  2. Question
  3. Physics
  4. A monoatomic ideal gas initially at 17° C is suddenly compressed to one eighth of its original volume. The temperature after compression is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

JIPMERJIPMER 1997

Solution:

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=1160\,K=887{}^\circ C $