Temperature Gradient of Pressure

a solid confined to constant volume at 0 Kelvin does not exert an increase in pressure on the container as the temperature is increased. 

For Cy/T to approach zero as T approaches zero, CV must go to zero at a rate at least proportional to T. Earlier, we summarized the temperature dependence of Cy on T for different substances and showed that this is true. For example, most solids follow the Debye low-temperature heat capacity equation of low T for which 

Thus Cp m and CVm differ little from one another at low temperatures. The Debye low-temperature heat capacity equation (and other low-temperature relationships) we have summarized calculates Cp.m, as well as CV. m, without significant error. 

At 0 Kelvin, both T and 5 are zero. Hence G0 = H0. This relationship will become important as we work with thermodynamic functions described at the end of this chapter. 

A number of techniques have been used to cool substances to low temperatures. Often, the process is done in steps one procedure is used to cool to a certain temperature, then a second cools to still lower temperatures, and so on. 

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