Cp-Cv=R derive
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It is Mayer\’s equation.Derivation:ΔU = ΔQ + ΔW ΔU = Cv ΔT (At pressure is constant)ΔQ = Cp ΔT (At pressure is constant)ΔW = -P ΔV (Negative since the calculation been complete)Pv = RT (1 mole of gas)Because of pressure is constant, R is also constantChange in V will make change in TPΔV = R ΔTCv ΔT = CpΔT – RΔTDivided by ΔTCv = Cp – RCp – Cv = R
U=q-wnr∆t=ncp∆t – ncv∆tr=cp-cv( n and ∆t will be cancelled out)