This is an ongoing question that I have used with my students for years yet there has always been a little voice telling me that I’m doing something wrong.
Start with ice at -20C and end with steam at 120C. How much heat is needed for this change? I break it up into five part.
The change in temp for the ice to get from -20C to 0C using the specific heat capacity of ice.
2)The change of state from ice to water using the heat of fusion of water.
The change in temp for the water to get from 0C to 100C using the specific heat capacity of water.
4)The change of state from water to steam using the heat of vapourization of water.
5)The change in temp for the steam to get from 100C to 120C using the specific heat capacity of steam.
Is this correct?
That will work to a very good approximation, but there are a couple of wrinkles.
First, the heat capacity varies slightly with temperature. For liquid water over the range 0 to 100 celsius, the variation is less than 1%.
Second, you need to specify what happens to the steam. If it’s confined to a constant volume (as in a stoppered vessel), the figure to use for the heat capacity is constant-volume heat capacity (C[sub]V[/sub] ). If the steam is allowed to expand at constant (usually atmospheric) pressure, use constant-pressure heat capacity (C[sub]P[/sub]). Constant-pressure heat capacity is larger than constant-volume heat capacity because some of the energy goes to displacing atmospheric molecules. For water vapor, C[sub]P[/sub] is about 34 J/K·mol and if steam can be treated as an ideal gas, C[sub]V[/sub] would be around 26 J/K·mol.