Heat is energy flow from high temperature to low temperature. Heat flow can result in temperature change or heat can flow into or out of the system without any change in temperature. To deal with this, it is best to break processes up into these two situations.
For the first, heat flows and the temperature changes. The amount of temperature change depends on the amount of heat and the heat capacity of the system. Heat capacity relates the temperature change to the amount of heat. Heat capacity (\(C\)) is an extensive property. The more material the higher the heat capacity. Therefore, when calculating an actual temperature change, it is important to know the heat capacity of the object you are working with.
\[q = C\Delta T\]
Here \(C\) is the heat capacity. The heat capacity has units of energy per temperature. Typically we will use J K-1. As it is an extensive quantity it is often tabulated in an intensive form. For example, you might want the heat capacity per mole. This is the molar heat capacity (\(C_{\rm m}\)). This will have units of J mol-1 K-1. Alternatively, the heat capacity might be the "specific heat capacity" (\(C_{\rm s}\)). This is the heat capacity per mass. This could have units of J g-1 K-1. As a result, some calculations require you to multiply the molar or specific heat capacity by the number of moles (\(n\)) or by the mass (\(m\)) of a substance. Pay attention to the units and you'll keep it straight. Here are the formulas for heat using molar heat capacity and specific heat capacity:
\[{\rm molar:} \hskip20pt q = n \;C_{\rm m}\; \Delta T \]
\[{\rm specific:} \hskip20pt q = m \;C_{\rm s}\; \Delta T \]
There can also be heat flow without temperature change. For this case, the energy that flows in or out is not changing the thermal kinetic energy, but instead it is changing the potential energy of the system. The potential energy can change if there is either a chemical change or a physical change such as a phase transition. We will address this further in the thermochemistry section.