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
21.4
B
31.4
C
41.4
D
51.4

Solution

## The correct option is B $${ 4 }^{ 1.4 }$$Given,$$n=5mole$$$$V_1=V$$$$V_2=\dfrac{V}{4}$$$$\gamma=1.4$$$$P_1=P$$For adiabatic process, gas equation is$$PV^{\gamma}=K$$ (constant)$$P_1V_1^{\gamma}=P_2 V_2^{\gamma}$$$$P_2=P_1\left(\dfrac{V_1}{V_2}\right)^{\gamma}$$$$P_2=\left(\dfrac{V}{V/4}\right)^{\gamma}P$$$$P_2=4^{1.4}P$$The correct option is C.Physics

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