Verified Solution • 2025–26 Session moderate

QJEEM23Ph0467: JEE Main 2023 Physics - Class 11 JEEM23Ph0467 Solution: A hypothetical gas expands adiabatically such that its volume…

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 1681\frac{16}{81} . Then the ratio of CpCv\frac{\mathrm{Cp}}{\mathrm{Cv}} will be.

Multiple Choice Options

  • A 31\frac{3}{1}
  • B 43\frac{4}{3}
  • C 12\frac{1}{2}
  • D 32\frac{3}{2}

Step-by-Step Verified Solution

Let γ\gamma be the ratio of CpCv\frac{C_{p}}{C_{v}}

Then for adiabatic process

amp;PVγ= Constant amp;⇒PiPf=(VfVi)γamp;⇒8116=(278)γamp;⇒γ=43\begin{aligned}& P V^{\gamma}=\text { Constant } \\\\& \Rightarrow \frac{P_{i}}{P_{f}}=\left(\frac{V_{f}}{V_{i}}\right)^{\gamma} \\\\& \Rightarrow \frac{81}{16}=\left(\frac{27}{8}\right)^{\gamma} \\\\& \Rightarrow \gamma=\frac{4}{3}\end{aligned}

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