- #1

- 1,529

- 594

- TL;DR Summary
- Do not understand a derivation in Physical Chemistry by McQuarrie and Simon.

The text derives [itex]C_p-C_v=nR[/itex] for ideal gasses. They start with $$H = U + PV = U + nRT$$ for ideal gas. Since U is only a function of temperature for an ideal gas, the right-hand side is only a function of temperature so $$\frac{dH}{dT} = \frac{dU}{dT} + nR$$. Now the text does something I don't understand.

First they set $$\frac{dH}{dT} = \left( \frac{\partial H}{\partial T}\right)_p = C_p$$ Why can they assume constant pressure here? I feel like I am missing something fundamental.

Similarly, they set $$\frac{dU}{dT} = \left(\frac{\partial U}{\partial T} \right)_V = C_v$$. Again, I don't understand why they can assume constant volume.

Any help would be much appreciated.

Thanks!

Jason

First they set $$\frac{dH}{dT} = \left( \frac{\partial H}{\partial T}\right)_p = C_p$$ Why can they assume constant pressure here? I feel like I am missing something fundamental.

Similarly, they set $$\frac{dU}{dT} = \left(\frac{\partial U}{\partial T} \right)_V = C_v$$. Again, I don't understand why they can assume constant volume.

Any help would be much appreciated.

Thanks!

Jason