derive cp-cv= R ????
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If q is the amount of heat involved in a system Then, at constant volume, q = qv = Cv∆T = ∆U …(i)
And at constant pressure. q = qp = Cp∆T = ∆H …(ii)
For one mole of an ideal gas (n = 1). Change in enthalpy ∆H = ∆U + ∆(pV) = ∆U + ∆(pT) ∆H = ∆U + R∆T …(iii)
On substituting the values of ∆H and ∆U in equation (iii) from equation (i) and (ii), Cp∆T = Cv∆T + R∆T Or Cp = Cv + R
Cp − Cv = R
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