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Q.

An ideal gas undergoes a process in which PV−a= constant, where Vis the volume occupied by the gas initially at pressure P. At the end of the process, rms speed of gas molecules has become a1/2 times of its initial value. What will be the value of CV so that energy transferred by the heat to the gas is 'a'times of the initial energy (ΔQ=aPV)

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a

(a2+1)Ra2−1

b

(a2+1)R(a2+1)

c

(a+1)R(a−1)

d

(a−1)R(a+1)

answer is A.

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Detailed Solution

ΔQ=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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