Question

A heat insulating cylinder with a movable piston contains 5 moles of hydrogen at standard temperature and pressure if the gas is compressed to quarter of its original volume when the pressure of the gas is increased by ($\gamma$ = 1.4 )

• A. $2^{1.4}$
• B. $3^{1.4}$
• C. $4^{1.4}$
• D. $5^{1.4}$

Answer 1

Answer: (C)

$4^{1.4}$

Given,

$n=5mole$

$V_1=V$

$V_2=\frac{V}{4}$

$\gamma =1.4$

$P_1=P$

For adiabatic process, gas equation is

$P{V}^{\gamma }=K$ (constant)

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$

$P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }$

$P_2={\left(\frac{V}{V/4}\right)}^{\gamma }P$

$P_2=4^{1.4}P$

The correct option is C.