An introduction to heat capacity

What is heat capacity?

Heat capacity is the way that we can measure energy and enthalpy by monitoring temperature changes.

Enthalpy

Energy is released by reactions – or, sometimes, taken in – in the form of enthalpy. Enthalpy is simply the heat generated, and “heat” manifests as temperature.

Remember: heat is the microscopic motions of molecules, their kinetic and potential energies combined. It’s often very very easy to think about heat as a substance flowing in and out of systems, but this is not the case.

Enthalpy and temperature

The enthalpy released by a reaction manifests as a temperature change. But while these are directly proportional, the proportionality constant is not always the same for each and every substance.

The proportionality constant here is the heat capacity. As an absolute measure, it is usually given in J K^-1. I.e. the amount of energy (in J) to raise something’s temperature by 1 K.

This is usually given a specific heat capacity, which is J K^-1 g^-1.

A more convenient measure of heat capacity

This measure is a significantly more convenient measure of heat capacity than a per-mole measure, simply because masses of substances and mixtures are more easily obtained.

It’s easier to think of 250 g of water (because we can weigh it) than 13.8 moles of water. We can also easily think about 250 g of saltwater, whereas “moles of saltwater” would be less rigorously defined.

Conditions

More important than the amount that we’re referencing heat capacity to is the conditions. Heat capacity at constant volume and constant pressure are two different things. Usually written C_v and C_p respectively.

Note: Subscripts in thermodynamics usually represent the variable that remains constant throughout a change. See the earlier articles about states and paths. This crops up in more advanced material, where the subscripts are added to some differential/calculus notation.

Equations

While I would entirely recommend checking the units of heat capacity in order to see what you do with it, it’s sometimes useful to see it as an equation:

[q=C_p times m times Delta T]

Where q = heat transferred, Cp = heat capacity at constant pressure, m = mass, ΔT = temperature change.

This can be rearranged to predict temperature changes from the energy that has been released.