Thermodynamics Teasers
Eduardo Sánchez Velasco
Truman State University
In the following questions cp and cv denote the molar specific heats at constant pressure and volume.
1.- Use available data to find the value of cp - cv for aluminum at room temperature. Is it close to R?
2.- Find a substance that, at some pressure and non zero temperature, has cp = cv .
3.- What is wrong with the following argument to prove that cp can never be less than cv?
At constant pressure some of the heat given to a substance has to be used to produce work as the substance expands. At constant volume there is no expansion and all the heat goes to increase the temperature of the substance. Therefore, we need less heat to increase the temperature by a certain amount if the volume is kept constant.
4.- What is the real reason why cp can never be less than cv for any substance?
5.- Search the literature to find a pure substance with negative latent heat of fusion (melting) in some region of its phase diagram (that is, we must GIVE latent heat to go from liquid to solid). Because the latent heat to go from the low temperature phase to the high temperature phase can not be negative, to get a negative latent heat of fusion, the solid must be the high temperature phase and the liquid the low temperature phase!
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