Heat content as a state function?

[firecool]

at 3:30 he introduces heat content to show why it can't be a state variable. he says that if q=2 is added to the cycle everytime you go around the cycle the heat content would be incremented by 2. but as heat=work shouldn't that extra 2 be lost as work and at point 1 you always have hc=5? watch the video to make sense of my question.. :)

 

[D H]

He's absolutely correct.

Another way to look at it. There are two cusps on that PV diagram connected by two different curved paths. Suppose the heat content of the point on the left is 5. What is the heat content of the point on the right? You will get a different answer for the upper path versus the lower one. You can't assign a heat content as a state variable to that point on the right because this supposed heat content depends on the initial state, the final state, and the path followed from the initial state to the final state. It is a path-dependent quantity.

A state variable, by definition, cannot depend on how the system attained its current state. A state variable is a function of the current state only.

 

[firecool]

cusps? :P

 

[D H]

Cusp: "A point at which the direction of a curve is abruptly reversed". Or a bit more generally, a point at which the gradient to the curve doesn't exist. There are two "cusps" in that PV diagram in the video, one on the left and one on the right.

 

[firecool]

thanks! :)