# cp and Cv!

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Hi all,

I read this a while ago and was wondering why the this was so; Cp>Cv for a gas while for solids its the same. I tried to do some research but got absolutely nothing. Any ideas.

Help appreciated.

thnx

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Cp is the value for the specific heat at constant pressure

Cv is the value for the specific heat at constant volume

A gas can be compressed, but a solid is (near) incompressible.

If you decide to keep the pressure constant, you can just assume that the volume will also remain constant. Therefore, the two must be the same.

Disclaimer - I did not get this from a thermodynamics book (which should be the right source). I just wrote it down because it seems logical to me. (i.e. I haven't done any research on it).

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captain panic is right.

although if you want to be super accurate about it or have a large temperature change where thermal expansivity of the solid becomes significant then you cannot assume they are the same.

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the idea about the Cp and Cv for solid has been established but for gases are you guys sayin that when a gas is compressed then we have changed the pressure so the volume is decreased and so does the Cp and vice versa? Sounds logically tough!

And by the way thanks guys .

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Eehm, almost. When a gas is compressed, then we changed the pressure. But we're not dealing with compression, we're dealing with a change of temperature.

If the temperature increases, and you have a rigid flask that cannot expand, the pressure will build, and the volume remains constant. If you heat something in a balloon that can expand, the volume will change and the pressure remains constant. In the 1st case, you use Cv, in the second, you use Cp.

Because it's often dangerous, and not very practical to allow pressure to build because of heating, Cp is the most used. It's the value that you'll find in handbooks.

Disclaimer: the following text does come from a Thermodynamics book (Smith & Van Ness) but also from wikipedia:

Definition for Cp, Cv

$C_V=\left(\frac{\partial U}{\partial T}\right)_V$

$C_P=\left(\frac{\partial H}{\partial T}\right)_P$

The subscript V and P mean "constant volume" and "constant pressure" respectively.

These two formulas indicate that the Cv deals with the internal energy (U), and the Cp deals with the enthalpy (H). The enthalpy is the parameter used for heat balances in engineering.

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