Sampat Kumar
Hi
As peteroznewman correctly mentioned, Cp and Cv are the same for the solid, so Cp is enough for the analysis and will work as expected. the Cp and Cv are important for the fluid, especially for the gases. let’s take two piston-cylinder arrangements.
Case -1 filled the solid inside the cylinder and applied the heat at constant volume and constant pressure. The molecules of the solid are very closely packed so, when we apply heat to the piston cylinder arrangement at constant pressure and volume then the expansion of the piston would be near zero. it means there is no work done, so the applied heat is converted into the system’s internal energy in both cases.
Qcp= Ui + W = Qcv
mCpdt= mCvdt ( Unit mass, same material and unit rise in temperature)
Cp= Cv= C
Generally, we consider Cp for the solid.
Case -2 Filled the same amount of gases inside cylinders and applied heat to the system at constant pressure and volume. Since at constant volume, the work done would be zero then the total heat at constant volume will be converted into internal energy of the system. When we apply heat to the system at constant pressure, then there will be some work done also with the rise in the internal energy, so there is much more heat required to change the same amount of temperature at constant pressure as compared to the constant volume.
Qcp>Qcv
mCpdt > mCvdt ( mass same, material property same, same rise in the temperature)
Cp> Cv
The different values of Cp and Cv will impact the result in the fluid especially for the gases because of the large expansion of the gases. so we have to consider both Cp and Cv for the gases.
I hope it will help you.
Regards,
Sampat
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