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## Main Question or Discussion Point

Hi everybody,

I have the following doubt. We know that for a thermodynamic system the following equality holds:

$$

C_P-C_V=-T\frac{\left[\left(\frac{\partial P}{\partial T}\right)_V\right]^2}{\left(\frac{\partial P}{\partial V}\right)_T}

$$

Now, the mechanical stability of the system requires that the volume decreases with increasing pressure, i.e. [itex](\frac{\partial V}{\partial P})_T<0[/itex]. So this seems to lead to [itex]C_P>C_V[/itex]. Is that always true? What happen if the temperature is negative, [itex]T<0[/itex]?

Thanks

I have the following doubt. We know that for a thermodynamic system the following equality holds:

$$

C_P-C_V=-T\frac{\left[\left(\frac{\partial P}{\partial T}\right)_V\right]^2}{\left(\frac{\partial P}{\partial V}\right)_T}

$$

Now, the mechanical stability of the system requires that the volume decreases with increasing pressure, i.e. [itex](\frac{\partial V}{\partial P})_T<0[/itex]. So this seems to lead to [itex]C_P>C_V[/itex]. Is that always true? What happen if the temperature is negative, [itex]T<0[/itex]?

Thanks