Cp=Cv+R(Cp=[dq/dt]p),(Cv=[dq/dt]v)So using first law of thermodynamicsdq=du+dwDividing both side by dtdq/dt=du/dt+dw/dt. dq=mL,dw=pdvat constant volume[dq/dt]v=[du/dt]v+[dw/dt]v[dq/dt]v=[du/dt]v+[pdv/dt]vTake constant term outside the bracket[dq/dt]v=[du/dt]v+p[dv/dt]vCv=[du/dt]v+0Cv=du/dt………………….. 1At constant pressure[dq/dt]p=[du/dt]p+[dw/dt]pCp=[du/dt]p+[pdv/dt]p……………………2From ideal gas equationPv=nRtn=1 for 1molePv=RtAt constant pR=pdv/dtPutting this value pdv/dt in eq 2Cp=Cv+RR=Cp-Cv. Mayer\’s formula
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