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Question

# The pressure of an ideal gas varies with volume as P=αV, where α is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes m times its initial volume. The work done by the gas in the process is

A
αV22(m21)
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B
α2(m21)
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C
α2V22(m21)
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D
αV2(m21)
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Solution

## The correct option is A αV22(m2−1)The work done by a gas is given by W=V2∫V1PdV In this case it is given that P=αV. Also if the initial volume V1 is V then the final volume V2 is mV So, W=mV∫VαVdV=α[V22]mVV E=α2[m2V2−V2] W=αV22(m2−1) So, option (a) is correct.

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