A) \[\frac{{{T}_{A}}}{{{T}_{B}}}={{10}^{\frac{7}{5}}}\]
B) \[\frac{{{T}_{A}}}{{{T}_{B}}}={{10}^{\frac{2}{5}}}\]
C) \[\frac{{{T}_{A}}}{{{T}_{B}}}={{10}^{\frac{4}{15}}}\]
D) \[\frac{{{T}_{A}}}{{{T}_{B}}}={{10}^{\frac{7}{15}}}\]
Correct Answer: C
Solution :
| For adiabatic process, |
| \[{{T}_{i}}{{V}_{i}}^{\gamma -1}={{T}_{f}}V_{f}^{\gamma -1}\Rightarrow \frac{{{T}_{f}}}{{{T}_{i}}}={{\left( \frac{{{V}_{i}}}{{{V}_{f}}} \right)}^{\gamma -1}}\] |
| Here, \[\frac{{{V}_{i}}}{{{V}_{f}}}=10\] |
| So, \[{{T}_{f}}={{T}_{i}}{{(10)}^{\gamma -1}}\] |
| For monoatomic gas, \[\gamma =\frac{5}{3}\]and for diatomic gas, and for \[\gamma =\frac{7}{5}.\] |
| Hence, \[\frac{{{T}_{A}}}{{{T}_{B}}}=\frac{{{10}^{\frac{5}{3}-1}}}{{{10}^{\frac{7}{5}-1}}}={{10}^{\frac{4}{15}}}\] |
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