# Maximum temperature

Consider the following problem: you are given two BODIES at temp TA and TB.Do you agree that the maximum possible work i can extract from them happens to be in the case when they are left with the equilibrium final temperature of sqrt(TA.TB). This minimizes the entropy and hence corresponds to the maximum possible work extractable from the system.this is consequently the minimum possible equilibrium temperature.
now, we im interested in the case of how its possible to attain maximum possible equilibrium temperature and what is its value? I think it would be when the bodies are placed next to each other such that the final temperature is (TA+TB)/2. In this case the useful work done would be zero, being entirely wasted to increase entropy.
do you agree?

## Answers and Replies

The equilibrium temperature will be when the two bodies are at the same temperature. Then the entropy of the two bodies will be maximal. The equilibrium temperature will be in between TA and TB. But the exact value depends on the masses and specific heath of both bodies. You will obtain the maximum temperature when the colder object is very small, but then, you won't obtain much work.

But the exact value depends on the masses and specific heath of both bodies. You will obtain the maximum temperature when the colder object is very small, but then, you won't obtain much work.

see, it is clearly stated that given that the specific heat is C, the answer is to be in terms of TA and TB. And yes when the entropy is maximal, the work is very less. If you plot entropy in terms of Teq, where Teq is the equilibrium temp, then u'll find it is monotonically increasing.

The question still remains, what is the maximal possible equilibrium temp, irrespective of the work done?