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• # The connection between heat energy and temperature

This article briefly talks about the connection between heat energy (enthalpy), and temperature: the concept of heat capacity.

## What is enthalpy (heat energy)?

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 (that’s how it used to be thought of, and the way we talk about it is still a holdover from that time!), but this is not the case.

## Enthalpy and temperature

Temperature and heat are directly proportional, the proportionality constant is not always the same for each and every substance. If we deliver a certain amount of heat to a beaker of ethanol, the temperature change will not be the same as if we delivered the exact same amount of heat energy to a beaker of water.

[Temperature propto Heat] [T propto q]

### The heat capacity

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

### A specific heat capacity

We also usually measure a specific heat capacity, which is J K-1 g-1. The amount of energy required to raise 1 g of the substance by 1 K. Note that, for heat capacity, we deal in per mass, not per mole.

This mass-based measure is a 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.

The heat capacity of an entire mixture also needs to be taken into account. We can easily think about 250 g of saltwater, whereas “moles of saltwater” would be less rigorously defined. Especially as the heat capacity of saltwater isn’t just a simple addition of the heat capacity of water and the heat capacity of salt.

## 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 Cv and Cp 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.  