By Rowland S. Benson and W. A. Woods (Auth.)

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For some substances either one or other of the specific heats can be determined experimentally but the other is somewhat difficult to determine. It is convenient to have some relationship between the specific heats whereby the experimental evaluation of one can be used to derive the other. The following procedure can be used for this purpose. We start with the equation of state s = s(T,v) ds = (If). and dT + 3S 3V dv. 25) we have »L * (B)T fasl [Trl and from ( 2 . 62) Once again we have the specific heats in terms of the p-v-T.

Similarly the coefficient of expansion (8) is dependent on the pressure and temperature, but for low pressures the effect of pressure is not significant. Whilst the isothermal compressibility (k) is always a positive number, this is not always the case for the coefficient of expansion (8). For ice and water, for example, at low temperatures 0 to 70°K and 273 to 277°K the coefficient (8) is negative. W. Zemansky for further details. 1. On the saturation curves there is a discontinuity in the slope of the p-v isotherm at all points except C.

8) will lead to the state equation in algebraic form. 9) which on integration gives p Y = constant, tin physics the linear coefficient of expansion (a) is n dT For an isotropic material 3 - 3a. + Looking a little deeper into our assumptions we see that the assumption k = 1/p leads to Boyle's Law and the assumption B = 1/T leads to Charles1 Law. Hence an ideal gas obeys Boylefs and Charles' Laws. Except f or this simple case it is not possible to obtain the state equation directly by the methods outlined above and empiri cal formulae based on experiment or theoretical molecular models are used.

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