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34 Physics Formulary by ir. J.C.A. Wevers For an ideal gas holds: C mp - C mV = R . Further, if the temperature is high enough to thermalize all internal rotational and vibrational degrees of freedom, holds: C V = 1 2 sR . Hence C p = 1 2 ( s + 2) R . For their ratio now follows γ = (2 + s ) /s . For a lower T one needs only to consider the thermalized degrees of freedom. For a Van der Waals gas holds: C mV = 1 2 sR + ap/RT 2 . In general holds: C p - C V = T p T V · V T p = - T V T 2 p p V T 0 Because ( p/ V ) T is always < 0 , the following is always valid: C p C V . If the coefficient of expansion is 0, C p = C V , and also at T = 0 K. 8.4 The laws of thermodynamics The zeroth law states that heat flows from higher to lower temperatures. The first law is the conservation of energy. For a closed system holds: Q = Δ U + W , where Q is the total added heat, W the work done and Δ U the difference in the internal energy. In differential form this becomes: d Q = dU + d W , where d means that the it is not a differential of a quantity of state. For a quasi-static process holds:
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