# Maximum Work for A engine

We are asked to find the maximum work obtainable from an engine. Which the engine operates between two reservoir, one at $$T_1$$ and another at $$T_2$$.

Given $$T_2 > T_1$$ , and the final common temperature is $$T_3$$.

My question is , do i need to consider the changing temperature of the reservoirs, or simply deriving the familiar equation $$1 - \frac{T1}{T2}$$ referring to our result ?

• Use a reversible heat engine (on the argument that irreversibility diminishes the extracted work), hence all heat moving out of one reservoir enters the other. This will tell you T3. Then get the efficiency using ideal case at each stage as the temperatures change (use tiny amounts of heat and do an integral). Sep 20, 2021 at 21:55

You probably are supposed to consider, that the reservoirs change their temperature (and therefore the process gets more and more inefficient towards the end). Otherwise the given $T_3$ would make no sense.

But you also need some more given values, like the heat capacity...

• The question indicated that the heat capacity is independent of temperature and being "C" for both reservoirs. Can you hint me where should i start ? I havn't encountered such question and my wild guess was to consider 'infinite Carnot cycle' ? Apr 18, 2016 at 15:14
• The hint to understand this is to think about what changes in the process. Take the efficiency factor of the Carnot process for each $\mathrm dQ$ which is pumped from the hot to the cold reservoir. But aside from the work done something else happens when $\mathrm dQ$ is transferred. You'll have to integrate in order to find $T_3$.
– Ilja
Apr 18, 2016 at 15:19
• If $T_3$ is given, then it's a different problem ... then think why it is not what one could expect for heat transfer between two equal bodies.
– Ilja
Apr 18, 2016 at 15:20

You can draw Carnot cycle for every instance that the reservoir temperatures changes. This would mean that the maximum work obtained per cycle would keep changing until it reaches equilibrium.