Q101 / 180 · AIIMS 2007 · Physics

In an adiabatic change, the pressure and temperature of a monoatomic gas are related as \(P \propto T^{\mathrm{C}}\), where \(C\) equals

  • A
    \(\frac{2}{5}\)
  • Correct answer
    B
    \(\frac{5}{2}\)
  • C
    \(\frac{3}{5}\)
  • D
    \(\frac{5}{3}\)

Solution

\(\gamma=1+\frac{2}{f}\) \(\Rightarrow \gamma\) for mono atomic gas \(=1+\frac{2}{3}=\frac{5}{3}\) For adiabatic relation \(\frac{P^{\gamma-1}}{T^\gamma}=\) constant, \(P \propto T^{\frac{\gamma}{\gamma-1}} \Rightarrow P \propto T^{\frac{5}{3} \times \frac{3}{2}}\) \(\therefore \quad T^C=T^{\frac{5}{2}} \Rightarrow C=\frac{5}{2}\).

Hence, the correct answer is option: 'B'.

Relevant Questions