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 then 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)

As the cylinder is a heat insulating i.e. no heat is allowed to be exchanged. Hence the process is adiabatic.
$\therefore P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
$\frac{P_2}{P_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma }$
Here $V_1=V,V_2=\frac{V}{4},P_1=P$ and $\gamma =1.4$
$\therefore \frac{P_2}{P}={\left(\frac{V}{V/4}\right)}^{1.4}={\left(4\right)}^{1.4}$
$\Rightarrow P_2={\left(4\right)}^{1.4}P$