MHT CET · Physics · Kinetic Theory of Gases
The molar specific heat of an ideal gas at constant pressure and constant volume is ' \(\mathrm{C}_{\mathrm{p}}\) ' and ' \(\mathrm{C}_{\mathrm{V}}\) ' respectively. If ' R ' is a universal gas constant and the ratio of ' \(\mathrm{C}_{\mathrm{p}}\) ' to ' \(\mathrm{C}_{\mathrm{V}}\) ' is \(\gamma\), then ' \(\mathrm{C}_{\mathrm{p}}\) ' is equal to
- A \(\left(\frac{\gamma-1}{\gamma+1}\right) \mathrm{R}\)
- B \(\frac{(\gamma-1) R}{\gamma}\)
- C \(\frac{\mathrm{R} \gamma}{(\gamma-1)}\)
- D \(\frac{\mathrm{R} \gamma}{(\gamma+1)}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{R} \gamma}{(\gamma-1)}\)
Step-by-step Solution
Detailed explanation
\( \mathrm{C}_{\mathrm{p}} - \mathrm{C}_{\mathrm{V}} = \mathrm{R} \) \( \frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{V}}} = \gamma \implies \mathrm{C}_{\mathrm{V}} = \frac{\mathrm{C}_{\mathrm{p}}}{\gamma} \)
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