# SI Units for Isothermal Incompressibility and Specific heat capacity at constant volume

I am looking for the SI units of isothermal incompressibility and specific heat capacity at constant volume.

What I found was that isothermal compression was measured in " $\mathrm{m^2}\ \mathrm{N^{-1}}$" so I'm guessing isothermal incompressibility would be the same?

I also found that specific heat capacity was " $\mathrm{J}\ \mathrm{K^{-1}}$"so is this the same units for constant volume also?

The units of a partial derivative $\displaystyle\left(\frac{\partial Y}{\partial X}\right)_Z$ are the units of $Y$ divided by the units of $X$. The units of $Z$ don't matter.

• Isothermal compressibility is $-\displaystyle\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_T$, so the SI units are reciprocal pressure, $\rm Pa^{-1}$ or $\rm m^2\ N^{-1}$.
• Heat capacity at constant volume is $\displaystyle\left(\frac{\partial E}{\partial T}\right)_V$, so its SI units are energy/temperature or $\rm J\ K^{-1}$. When you say specific heat capacity, that means per unit mass, so the specific heat capacity at constant volume is $\rm J\ kg^{-1} K^{-1}$.

By specific heat capacity at constant volume, do you mean $c_v$? If so the units should be J/kgK.

If by isothermal incompressibility you mean the coefficient of isothermal compressibility found here, it looks like the units you have is correct (1/Pa).

## protected by Community♦Nov 14 '17 at 0:08

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