34Physics Formulary by ir. J.C.A. WeversFor an ideal gas holds:Cmp-CmV=R. Further, if the temperature is high enough to thermalize all internalrotational and vibrational degrees of freedom, holds:CV=12sR. HenceCp=12(s+ 2)R. For their ratio nowfollowsγ= (2 +s)/s. For a lowerTone needs only to consider the thermalized degrees of freedom. For aVan der Waals gas holds:CmV=12sR+ap/RT2.In general holds:Cp-CV=T∂p∂TV·∂V∂Tp=-T∂V∂T2p∂p∂VT≥0Because(∂p/∂V)Tis always<0, the following is always valid:Cp≥CV. If the coefficient of expansion is0,Cp=CV, and also atT= 0K.8.4The laws of thermodynamicsThe zeroth law states that heat flows from higher to lower temperatures. The first law is the conservation ofenergy. For a closed system holds:Q=ΔU+W, whereQis the total added heat,Wthe work done andΔUthe difference in the internal energy. In differential form this becomes:dQ=dU+dW, wheredmeansthat the it is not a differential of a quantity of state. For a quasi-static process holds:
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