The correct option is B T0(P0+ρlg(H−y)P0+ρlgH)2/5
As there is no exchange of heat, the process is adaibatic.
For an adiabatic process, TP1−γγ=constant
⇒T1P1−γγ1=T2P1−γγ2
Substituting,
P1=P0+ρlgH and P2=P0+ρlg(H−y) and γ=53 and 1−γγ=1−5353=−25
T2=T1(P1P2)−25=T1(P2P1)25=T0(P0+ρlg(H−y)P0+ρlgH)25