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 $