The discussion revolves around the requirement of constant temperature in the proof of the inequality \( dw \leq -dA \) for isothermal work in thermodynamics, particularly in the context of Helmholtz free energy. Participants explore whether this condition is necessary and the implications of temperature variations during the process.
Participants express differing views on the necessity of constant temperature in the proof, indicating that multiple competing perspectives remain unresolved.
The discussion highlights potential limitations in the assumptions made regarding temperature constancy and the implications for the derivation of the inequality, but does not resolve these issues.
Nikitin said:yes, but you could get the equation ##dw \leq-dA## without assuming T=constant anywhere?
I mean, from what I can see, all they do is use the 1st law of thermodynamics and the general fact that ##dQ \leq TdS##. So shouldn't the result they get, ie ##dw \leq-dA##, apply regardless if T is constant or not during the whole process?
stevendaryl said:Well, the differential equality for Helmholtz free energy is:
dA = -S dT -p dV = -S dT - dW
It seems to me that if T is not constant, then the term -S dT could be either positive or negative, depending on whether the temperature is increasing or decreasing.