InterviewSolution
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InterviewSolution
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An ideal gas is made to undergo a process `T = T_(0)e^(alpha V)` where `T_(0)` and `alpha` are constants. Find the molar specific heat capacity of the gas in the process if its molar specific heat capacity at constant volume is `C_(v)`. Express your answer as a function of volume (V). |
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Answer» By first law of thermodymanics `Q=dU+W` `impliesnCdT=nC_(V)dT+PdV` `impliesC=C_(V)=(PdV)/(ndT)=C_(V)+(RT)/(V)(dV)/(dT)` `impliesC=C_(V)+R((dV//V)/(dT//T))` . . . (i) Process equation is given as `T=T_(0)e^(alphaV)` . . . . (ii) Tke log of equation (ii), we get `log" "T=log" "T_(0)+alphaV` ltBrgt `implies(dT)/(T)=0+alpha" "dV` (Differentiating) `implies(dT)/(T(dV))=alpha` `impliesC=C_(V)+R(dV)/((V(dT)/(T)))=C_(V)=R(dV)/(V.alphadV)=C_(V)+(R)/(alphaV)` `impliesC=C_(V)+(R)/(alphaV)`. |
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