JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2024
- Hard
- MCQ
During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of \(\frac{C_p}{C_V}\) for the gas is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P} \propto \mathrm{T}^3\)
\(\mathrm{PT}^{-3}=\text { constant }\)
\(\because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text { constant from ideal gas equation }\)
\((\mathrm{P})(\mathrm{PV})^{-3}=\text { constant }\)
\(\mathrm{P}^{-2} \mathrm{~V}^{-3}=\text { cosntant } \quad . .(1)\)
\(\because \text { Process equation for adiabatic process is }\)
\(\mathrm{PV}^y=\text { constant } \quad . .(2)\)
\(\text { Comparing equation (1) and (2) }\)
\(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{V}}}=\mathrm{y}=\frac{3}{2}\)
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