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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
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B
31.4
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C
41.4
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D
51.4
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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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