# Molar specific heat

What is the difference between molar specific heat and molar specific heat at constant pressure?

It seems that both of them have the same formula, i.e

$$\frac{1}{n}\left(\frac{\mathrm dQ}{\mathrm dT}\right)$$

Then what is the difference between these two and why do they have the same notation?

• The difference is in the tiny index $\mathfrak p$ outside of the brackets. Why did you skip it? – Ivan Neretin Dec 25 '17 at 11:36
• Yes but that $p$ does not change the value of the formula right ? So you mean that both of them are essentially the same ? How is that possible ? – Aditi Dec 25 '17 at 11:46
• Yes it does change the result, and not by negligible amount. Ever heard about the specific heat at constant volume? – Ivan Neretin Dec 25 '17 at 11:49
• Sorry , I think I understood what you meant to say. Is it that the subscript $p$ denotes that pressure is held constant during differentiation and that gives specific heat at constant pressure. But for specifically for molar specific heat we do not include a subscript which means nothing is held constant during differentiation I believe ? – Aditi Dec 25 '17 at 12:00
• "Molar specific heat" is not a thing at all. Or rather, it is an umbrella term which means both $c_p$ and $c_V$ at once, much like the word "human" means you and me, and quite a few others. It has no value. Say, you know your weight, but what is the weight of a human? – Ivan Neretin Dec 25 '17 at 12:02

First of all it is important to indicate which properties of your system stay constant during the partial differentiation. Therefore you get the molar specific heat at constant pressure as $$\frac{1}{n}\left(\frac{\partial Q}{\partial T}\right)_p$$ and at constant volume $$\frac{1}{n}\left(\frac{\partial Q}{\partial T}\right)_V$$