Q:

I start with a closed container of pure steam at 100C and 1 atmosphere (saturated). Now I add heat to it without changing the volume (pressure increases). Common sense tells me that it will become unsaturated, but will it? If you heat steam at a constant pressure, it becomes unsaturated. If you increase pressure at a constant temp, it goes supersaturated. So which one wins? Do some gasses go the opposite way?

- Steve Flarity (age 57)

Phoenix, AZ

- Steve Flarity (age 57)

Phoenix, AZ

A:

That's a very nice clear question. Your common sense is right. There are fancy ways to make the argument but I think a simple approach will show why the conclusion is right for other vapors too.

Right at the equilibrium point, the entropy gain from a molecule leaving the liquid and joining the gas just balances the energy gain in the free energy expression F= E-TS, where E is energy, T is absolute temperature, and S is entropy. Now if you increase T, the entropy term becomes more important, so that favors forming the gas. (F is minimized in equilibrium.) So heating the saturated gas at fixed volume will make it less-than-saturated, even though it increases the pressure.

Mike W.

Right at the equilibrium point, the entropy gain from a molecule leaving the liquid and joining the gas just balances the energy gain in the free energy expression F= E-TS, where E is energy, T is absolute temperature, and S is entropy. Now if you increase T, the entropy term becomes more important, so that favors forming the gas. (F is minimized in equilibrium.) So heating the saturated gas at fixed volume will make it less-than-saturated, even though it increases the pressure.

Mike W.

*(published on 09/10/2012)*