In which of the following processes is energy transferred into the substance by work ($w > 0$)?
a) Expansion of a gas against the surroundings
b) Expansion of a gas into a vacuum
c) Vaporization of one mole of water at 50˚C in an open container
d) Melting of 100 g of ice on a laboratory benchtop
e) Combustion of methane in a constant volume container.
The correct answer is given as (d), but I needed to find a physicist to explain it to me. This problem can being thought of entirely in terms of thermodynamic work.
So, we know that
$w = P \Delta V$
From this, we see that no work is done in (b) and (e). Also, since the gas expanded against its surroundings, it did work on it's surroundings, which isn't what the question asked, thus (a) is not the correct answer.
Now, although (c) appears to be a heat transfer, and it is, there is a little more going on. The heat that was given to the water is converted into work as the water vaporizes, this causes a volume expansion (the gas rising). Intuitively, one can think of the surroundings as a tube with a movable piston. When vaporizing, the water vapor will push against the piston, increasing the pressure and thus the piston will move, causing the water to do work.
The last choice is (d), the correct answer, but there is also an intuitive way to think about this. As the ice is heated, it melts (this process is also, as we correctly deduced, is a heat transfer), however, this heat also causes the surrounding atmosphere to do work on the ice.
Again, think of a tube with a movable piston with a cube of ice that is slowly melting in the presence of normal air. As the ice melts, the volume will decrease, and thus the nitrogen and oxygen molecules in the air have more space to move about, decreasing the pressure, which causes the piston to move down, thus doing work upon the ice.
Hopefully this makes sense to everyone who has been either watching or contributing to this discussion.