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