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

Initial pressure and volume of a gas (&gamma; = 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 (A) 1P (B) 2P (C) 4P (D) 8P

Tardigrade Admin · Accepted Answer

For Isothermal expansion P1V1=P2V2 PV=P2× (4 V) P2=(P/4) For Adiabatic expansion P2V2&gamma; =P3V3&gamma; ((P/4))(4 V)&gamma; =P3(V)&gamma; P3=P4&gamma; - 1 P3=P41.5 - 1 ∴ P3=2P

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

$1 P$

$2 P$

$4 P$

$8 P$

For Isothermal expansion
$P_{1} V_{1} = P_{2} V_{2}$
$P V = P_{2} \times (4 V)$
$P^{2} = \frac{P}{4}$
For Adiabatic expansion
$P_{2} V_{2}^{γ} = P_{3} V_{3}^{γ}$
$(\frac{P}{4}) (4 V)^{γ} = P_{3} (V)^{γ}$
$P_{3} = P 4^{γ - 1}$
$P_{3} = P 4^{1.5 - 1}$
$∴ P_{3} = 2 P$

Q. 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

1P

2P

4P

8P