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Find the relatio between volume and temperature of a gas in a process, in which the molar heat capacity C varies with temperature T as `C=C_(V)+alphaT`. [`alpha` is a constant] . |
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Answer» By first law of thermodymanics, molar specific heat is given as `C=C_(V)+R((dV//V)/(dT//T))` . . . . (i) Compare (i) with given equation `C+C_(V)+alphaT=C_(V)+R((dV//V)/(dT//T))` `impliesR(dV//V)=alphaT((dT)/(T))` `implies(dV)/(V)=(alphadT)/(R)` `implieslog" "V=(alphaT)/(R)+logC` `implieslogV=log_(e)e(alphaT)/(R)+logC` `implieslog" "V=log[C.e^(alphaT//R)]` `impliesVe^(-alphaT//R)=C`. |
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