# What are the units of molar heat capacity for a process carried out at constant volume ($C_v$) for a monoatomic ideal gas?

I'm confused about what the units of $$C_v$$ for an ideal monoatomic gas are if we derive its value from the formula : $$C_v = \frac{f}{2}R$$ where $$f$$ represents the degree of freedom at room temperature.

(Wondering if they are $$\frac{L.atm}{mol.K}$$ or $$\frac{J}{mol.K}$$ if we use the above formula).

I encountered this in a problem which asked the change in enthalpy for a given process ($$\triangle H$$) under irreversible conditions and I used the formula $$\triangle H = nC_v\triangle T$$ but got the units wrong . Thank you in advance!

• Weird units for R. Have you had a look at the Wikipedia entry: en.wikipedia.org/wiki/Gas_constant Sep 17 at 20:39
• @Martin-マーチン do you mean that its units depend on what units I've taken for R? Sep 18 at 2:26
• @Martin-マーチン I have seen this unit for R only here on CH SE, multiple times, derived from R = pV/(nT) Sep 18 at 5:13
• If a tree has the height 5 m and if another tree is three times taller, can it have height 15 cm ? Sep 18 at 5:28
• For an ideal gas, $\Delta H=nC_p\Delta T$. However, if the process is irreversible, such the initial equilibrium pressure, the final equilibrium pressure, and the external pressure throughout the process are all not equal, then $\Delta H$ is not equal to Q. Sep 18 at 11:20