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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Infinity Learn · Accepted Answer

Δ$$Q=aPV$$;$$ncdT=anRT$$  $$cdT=aRT$$→(1) ∴ polytropic $$processC=CV+R1$$−x; $$C=CV+R1+a$$→(2)      Sub (2) in $$(1)Given$$ $$Vrmsf=a12Vrmsi$$     ∴$$Tf=aTi$$;$$dT=aT$$−TBy solving above equations $$CV=(a2+1)Ra2$$−$$1$$

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