From the equation Cp = Cv + T*(partial(p)/partial(t))V*(partial(v)/partial (t))P

Question

From the equation Cp = Cv + T*(partial(p)/partial(t))V*(partial(v)/partial (t))P

Van der waals equation: P = (nRT)/(v-nb) - (n^2a)/(V^2)

Prove thatCp - Cv = nR

Explanation / Answer

Consider a thermodynamic process in which a gas is heated. Case 1:constant volume: DU=Q+dW Here dW = 0 Hence dU=Q=Cp.dT ....(1) (from definition) Case 2:at constant pressure, gas is heated so that the same change in internal energy takes place. Then dU = Q + dW Q = Cv.dT Hence dU = Cv.dT + R.dT (dW = p.dV = R.dT) Substituting from (1), we get Cp.dT = Cv.dT + R.dT =>Cp = Cv + R, Which is the required result A quasi-static process (meaning nearly static) or quasi equlibrium process is a process in which the system is in equilibrium throughout the process, ie the process is infinitly slow. The change in temperature and pressure of the system with its surroundings is infinitesimally small. It is just a hypothetical concept to apply the thermodynamical laws in an easy way.

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