1. Tardigrade
  2. Question
  3. Physics
  4. Initial pressure and volume of a gas (γ = 1.5) are P and V respectively. First, it is expanded isothermally to volume 4V and then compressed adiabatically to volume V . The final pressure of the gas will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Initial pressure and volume of a gas $\left(\gamma = 1.5\right)$ are $P$ and $V$ respectively. First, it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$ . The final pressure of the gas will be

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

For Isothermal expansion
$P_{1}V_{1}=P_{2}V_{2}$
$PV=P_{2}\times \left(4 V\right)$
$P^{2}=\frac{P}{4}$
For Adiabatic expansion
$P_{2}V_{2}^{\gamma }=P_{3}V_{3}^{\gamma }$
$\left(\frac{P}{4}\right)\left(4 V\right)^{\gamma }=P_{3}\left(V\right)^{\gamma }$
$P_{3}=P4^{\gamma - 1}$
$P_{3}=P4^{1.5 - 1}$
$\therefore P_{3}=2P$