Notes for the Physics GRE - Harvard University Department of Physics

Force is related to pressure and area by F = P dA, sodW = −P dV (172)for a reversible process. Thus, the total work done on a system is,∫ V2W = − P dV. (173)V 1The adiabatic free expansion is not reversible, and there is no work done on thesystem and no change in entropy. For a wire:The first law of thermodynamics:dW = F dx. (174)∆U = W + Q, (175)where U is the internal energy of the system, W is the work done on the system,and Q is the heat added to the system. For a reversible process,The heat capacity:C =The specific heat c = C/m. C VC P is the heat capacity at constant pressure,Here, H = U + P V is the enthalpy. γ is defined by,dU = dQ − P dV. (176)lim Q/∆T = dQ/dT. (177)∆T →0is the heat capacity at constant volume,C V = dQ V /dT = ( ∂U∂T ) V . (178)C P = dQ P /dT = ( ∂H∂T ) P . (179)γ = C PC V> 1. (180)For an ideal gas,C P = C V + nR. (181)For a monotomic ideal gas,For an adiabatic free expansion,U = 3 2 nRT , C V = 3 2 nR , γ = 5 3 . (182)W = 0 , Q = 0 , ∆U = 0. (183)25