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Ideal Gas Equation

An ideal gas ...

Question

An ideal gas expands in such a manner that its pressure and volume can be related by equation, ${P V}^{2} =$ constant. During this process, the gas is

A

heated.

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B

cooled.

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C

neither heated nor cooled.

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D

first heated and then cooled.

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Solution

The correct option is B cooled.
$P V^{2}$ =constant
From ideal gas equation, PV=nRT
$\Rightarrow$ VT=constant
$\Rightarrow$ V is inversely proportional to T
$\Rightarrow$ expansion causes cooling
$\Rightarrow$ gas is cooled

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