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$n$ moles of an ideal gas undergo a process in which the temperature changes with volume as $T = K V^{2}$ .The work done by the gas as the temperature changes from $T_{0}$ to $4 T_{0}$ is:

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a

3nRT0

b

(5/2)nRT0

c

(3/2)nRT0

d

Zero

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detailed solution

Correct option is C

T=KV2 dT=2kVdV dV=(dT2KV) Further, P=nRTV Now. W=∫pdV=∫(nRTV)(dT2KV) =∫T04T0nR2 dT (as KV2=T ) =3nRT02

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An ideal gas undergoes a process in which $P V^{- a} =$ constant, where $V$ is the volume occupied by the gas initially at pressure $P$ . At the end of the process, rms speed of gas molecules has become $a^{1 / 2}$ times of its initial value. What will be the value of $C_{V}$ so that energy transferred by the heat to the gas is $' a'$ times of the initial energy $(Δ Q = a P V)$

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