# How possibly can heat flow between equally hot bodies?

1. Oct 2, 2015

### Omar Nagib

An ideal Carnot engine is composed of two reservoirs and a working fluid. The hot Reservoir and the cold one have temperatures $T_1$ and $T_2$ respectively, with $T_1>T_2$. The working fluid is in a phase transition and has temperature $T_1$ at the start of the Carnot cycle. It undergoes another phase transition at $T_2$ at the end of the cycle to return to its original state.

This is a P-V diagram of the Carnot cycle which proceeds in fours steps:

I'm particularly interested in the two stages (from 1 to 2) and (from 3 to 4). They can be described as follows:

1) Stage (from 1 to 2) is an reversible isothermal expansion of the working fluid to transform from the liquid state to the gaseous one. The working fluid is at $T_1$ and it happens to have boiling point at $T_1$; Hence heat $Q_1$ is supplied to the fluid from the hot reservoir until it transforms to a gas keeping its temperature constant along the whole process.(that the fluid's temperature is constant during the whole process is owing to it being in a phase transition).

2) Stage (from 3 to 4) is an reversible isothermal compression, and its similar to what we have just described, with the difference being in this case, heat $Q_2$ is drawn out of the fluid and transfers to the cold reservoir and the fluid transforms from gas to liquid retaining a constant temperature of $T_2$ throughout the whole process

I'm puzzled by the mechanism by which the working fluid undergoes phase transition. So at stage (from 1 to 2), both the fluid and the hot reservoir have the exact temperature, so that they're in a thermal equilibrium; Hence there should be no heat or energy exchange between the two bodies. The same can be said of stage (from 3 to 4).

So how is it possible for heat to flow from two bodies having the exact same temperature?

2. Oct 2, 2015

### Staff: Mentor

Hi Omar,

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