Question

An ideal gas of volume V and pressure P expands isothermally to volume 16V and then compressed adiabatically to volume V.The final pressure of gas is(value of gamma=1.5)-

Answer 1

Answer: The final pressure is 4P

Explanation:

During isothermal expansion: (Temperature T= constant)

$P_iV_i=P_fV_f$

It is given that,

$P_i=P, V_i=V, V_f=16V$

$P_f=\frac{PV}{16V}=\frac{P}{16}$

During adiabatic compression: (final volume is V)

$P_fV_f ^{\gamma}=P_{ff}V_{ff} ^{\gamma}$

$\gamma=1.5$

$\Rightarrow \frac{P}{16}(16V)^{1.5}=P_{ff} V^{1.5}\\ \Rightarrow P_{ff}=\sqrt{16}P=4P$

Hence, the final pressure of gas is 4P.