Reference: Daniel V. Schroeder, An Introduction to Thermal Physics, (Addison-Wesley, 2000) – Problem 1.50.
We can find how much heat is emitted or absorbed by a chemical reaction by working with the enthalpy of the reactants and products. For example, consider the combustion of methane with oxygen at a constant temperature of :
Using the table at the back of Schroeder’s book, for the formation of methane from elemental carbon (solid) and hydrogen (gas) is
for the dissociation of methane into its elements is therefore the negative of this.
The total enthalpy change for the creation of the products in reaction 1 from their elements is
for the reaction as a whole is
We can see this as follows. Suppose the absolute enthalpy of the elemental components (carbon, hydrogen and oxygen) is and of the reactants and products and . Then
In 1, if all 4 compounds are gases and the temperature is the same on both sides, there is no volume change, as there are 3 moles of gas both before and after the reaction. Therefore the entire enthalpy change is due to change in internal energy and, assuming no ‘other’ work is done, all this energy is emitted as heat. That is, for one mole of methane
If the water is produced as liquid instead of vapour, then (from the table in Schroeder), and
This time, the final volume is of the initial volume, since the 2 moles of water has condensed out as liquid with negligible volume compared to the gases. Thus the atmosphere does work
The change in internal energy is therefore found from
where is the temperature in centigrade, so here. This gives a value of so for 2 moles (around 36 g) of water, we have . The difference from the calculations here is only about 83 kJ, but I’m not sure how accurate the various values and formulas are. At least it’s close.
As a final example, suppose the Sun with a mass of around and luminosity of used the combustion of methane and oxygen as its energy source. The molar weights of methane and molecular oxygen around 16 g and 32 g so if the Sun were composed of one part methane to two parts oxygen (by molecular number), then the mass ratio is around methane:oxygen = 1 : 4. The number of moles of methane in the Sun is therefore
Assuming the water is produced as vapour, the Sun could produce a total energy of
so it would burn out after a time interval of
We can be pretty sure the Sun’s source of power isn’t chemical reactions!