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In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $V T = K$ , where $K$ is a constant. In this process, the temperature of the gas is increased by $∆ T$ . The amount of heat absorbed by gas is ( $R$ is gas constant)

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$\frac{1}{2} ∆ T$

$\frac{1}{2} R ∆ T$

$\frac{3}{2} R ∆ T$

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answer is B.

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Detailed Solution

$V T = K, V (\frac{P V}{R}) = \frac{P V^{2}}{R} = K =$ constant

For a polytropic process

$C = \frac{R}{1 - x} + C_{V} = \frac{R}{1 - 2} + \frac{3 R}{2} = \frac{R}{2}$

$∆ Q = \frac{1}{2} R ∆ T$

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