- #1
WWCY
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- 12
Hi all, I have had the following question in my head for quite a while:
Thermodynamic potentials written in differential form look like
$$dU = TdS - PdV$$
and we can obtain equations for say, temperature by doing the following partial
$$T = \frac {\partial U}{\partial S} |_V$$
Does this mean that this equation for temperature is only valid in a system where volume is held fixed? That is to say, can I only use the equation obtained in relation to experiments whereby volume doesn't change throughout?
My intuition tells me that it's not the case, and that it's simply stating that we are doing a partial derivative of ##U## with respect to ##S##, while leaving the ##V## variable untouched. However I keep getting a niggly feeling that I'm wrong.
Assistance is greatly appreciated.
Thermodynamic potentials written in differential form look like
$$dU = TdS - PdV$$
and we can obtain equations for say, temperature by doing the following partial
$$T = \frac {\partial U}{\partial S} |_V$$
Does this mean that this equation for temperature is only valid in a system where volume is held fixed? That is to say, can I only use the equation obtained in relation to experiments whereby volume doesn't change throughout?
My intuition tells me that it's not the case, and that it's simply stating that we are doing a partial derivative of ##U## with respect to ##S##, while leaving the ##V## variable untouched. However I keep getting a niggly feeling that I'm wrong.
Assistance is greatly appreciated.