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Standard XII

Physics

Ideal Gas Equation

A closed cont...

Question

A closed container of volume V contains an ideal gas at pressure P and Kelvin Temperature T. The temperature of the gas is changed to 4T due to passing heat to the container. Choose correct pairs of pressure and volume after change of the temperature.

P a n d V

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P a n d \frac{1}{2} V

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4 P a n d 4 V

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4 P a n d V

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\frac{1}{4} P a n d V

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Solution

The correct option is D $4 P a n d V$
As the container is closed, thus the volume of the gas remains constant i.e $V$
Using ideal gas equation, $P V = n R T$ $⟹$ $\frac{P}{T} = \frac{n R}{V} = c o n s t a n t$
$∴$ $\frac{P}{T} = \frac{P^{'}}{T^{'}}$ where $T^{'} = 4 T$

OR $\frac{P}{T} = \frac{P^{'}}{4 T}$ $⟹ P^{'} = 4 P$
Hence the final pressure and volume of the gas is $4 P$ and $V$ respectively.

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A closed container of volume V contains an ideal gas at pressure P and Kelvin Temperature T. The temperature of the gas is changed to 4T due to passing heat to the container. Choose correct pairs of pressure and volume after change of the temperature.

The correct option is D 4PandVAs the container is closed, thus the volume of the gas remains constant i.e VUsing ideal gas equation, PV=nRT ⟹ PT=nRV=constant∴ PT=P′T′ where T′=4TOR PT=P′4T ⟹P′=4PHence the final pressure and volume of the gas is 4P and V respectively.