Using specific heat at different conditions [closed]








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Why can the change in energy of an ideal gas system (through a process in which V is not constant), still be calculated using Cv? (as in DE=Cv\*DT)




The subscripts v and p refer to how these heat capacities **are measured** experimentally, not how they are applied in practice. In each case, the heat capacity can be measured by determining how much heat has to be added to the system in either a constant volume experiment or in a constant pressure experiment. On the other hand, for an ideal gas, irrespective of whether the experiment is carried out at constant pressure or at constant volume, the changes in internal energy and enthalpy are given by dU=CvdT and dH=CpdT. This is because U and H are functions only of T for an ideal gas. The general mathematical definitions of these heat capacities are $$C\_v=\left(\frac{\partial U}{\partial T}\right)\_v$$$$C\_p=\left(\frac{\partial H}{\partial T}\right)\_p$$If you are not dealing with an ideal gas, then the volume or the pressure also affect U and H, and this must be accounted for. But, for an ideal gas, only the temperature change is required to determine the changes in U and H.


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