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Heat capacity is very much what it sounds like, so let's break down the term. Heat is a type of energy based on the random kinetic movements of molecules. Heat is closely related to temperature, but it is important to understand that they are not the same thing. Just because an object has a lot of heat, does not ensure it has a high temperature, and vice versa. Hopefully this document will help you to understand why that statement is true. Capacity means how much something is able to contain. Putting these two terms together, heat capacity gives a sense of how efficiently an object can store heat energy.

Heat capacities are measured in units of energy per temperature, i.e. $\frac{\text{J}}{\text{k}}$. Sometimes the are expressed in energy per mass-temperature (i.e. $\frac{\text{J}}{\text{g}\cdot\text{k}}$), but this is referred to as the specific heat capacity. So the heat capacity of an object says how much energy you need to put in to the object in order to raise the temperature by 1 degree.

Heat capacities can vary wildly between objects and materials. For example, gold has a specific heat capacity of $0.385 \text{ } \frac{\text{J}}{\text{g}\cdot\text{k}}$, but water has a specific heat capacity of $4.184\text{ } \frac{\text{J}}{\text{g}\cdot\text{k}}$. As we can see, two objects at the same temperature can have wildly different heats. Moving forward it is important to realize that objects will reach a temperature equilibrium, not a heat equilibrium.

(Video) What Is The Difference Between Specific Heat Capacity, Heat Capacity, and Molar Heat Capacity

by The Organic Chemistry Tutor

In this video, The Organic Chemistry Tutor describes heat capacity. First, you'll learn the difference between heat capacity, specific heat capacity, and molar heat capacity. He'll show you each equation and work through two example problems. This video will help clarify heat and heat capacity.

Previously, we studied the relationship between heat and temperature. Heat is the transfer of kinetic energy via atomic or molecular collisions. The temperature is the state variable that indicates heat transfer. For example, we know that chemical reactions can be exothermic or endothermic. In an exothermic reaction, energy gets transferred from the system to the surroundings. So, the temperature increases. In endothermic reactions, it's the opposite. But what's the quantitative connection between heat and temperature? That's what we'll explore in this lesson!

Heat Capacity

We know that when an object is heated, there is an energy transfer. We observe that energy transfer via the temperature change. But how much energy is required to raise the temperature? As you might guess, it depends on the object. For example, we know that metals are often good conductors. That's because of their metallic bonding. So, we would expect their temperature to increase with very little heating. And we see exactly that! For example, imagine I had 5.0 grams of aluminum and 5.0 grams of water. To raise the aluminum's temperature by one Kelvin would require 4.5 joules of energy. But, the water needs 20.9 joules. That's a huge difference!

But how did I get those numbers? I used the heat capacity. The heat capacity is the energy required to raise an object's temperature by one Kelvin. So, it has units of joules per Kelvin ($\frac{J}{K}$). The problem is that the term object is somewhat vague. We can't define a heat capacity for every object in the world. That's just too much! Instead, we use the specific heat capacity. We'll study it more in a future lesson. But it's the energy needed to raise the temperature of one gram of a substance. It has units of joules per gram-kelvin ($\frac{J}{gK}$). So, how did I calculate the energy needed to heat 5.0 grams of aluminum and water? I used their specific heat capacities.

Factors Influencing Heat Capacity

We've seen that different materials can have big differences in their heat capacities. But what causes the difference? In our example, why did water require much more energy than aluminum? It depends on the substance's chemical properties.

Let's consider the most simplistic model. Let's imagine we have one mole of helium gas in a container. Helium is a noble gas. So, it doesn't form bonds and has minuscule intermolecular interactions. It meets all the criteria for being an ideal gas. What would happen if we heated our helium gas? The atoms would translate faster. They would have an increase in kinetic energy. So, our temperature would increase.

Now, let's consider a diatomic gas, like hydrogen gas. Again, the intermolecular interactions are tiny. But, this time, there is a covalent bond. What happens when we heat the gas? The molecules will again translate faster. But, the molecules can also rotate around the center of mass. The rotation is still a form of kinetic energy. But, a diatomic gas has various expressions of kinetic energy. So, how would it compare to a monoatomic gas? It would require more energy to achieve an equal average kinetic energy. In other words, it takes more energy to reach the same temperature. Why? Because the kinetic energy gets averaged across multiple kinds of motions. The fancy term for the different types of movement is degrees of freedom. So, the more degrees of freedom a molecule has, the greater its heat capacity.

Now let's consider molecules with strong intermolecular forces. Water is a great example! We've already seen that water has a specific heat capacity of $4.18 \frac{J}{gK}$. That's a large heat capacity! Why? Because water hydrogen bonds. We know that more powerful intermolecular forces resist the molecule's movement. So, it takes more energy to increase the average kinetic energy.

Heat Capacity Equations

At this point, are you wondering how we use the heat capacity? It turns out that we have two equation that uses heat capacity. The first relates the heat capacity to the internal energy and temperature. The equation is $C=\frac{\Delta U}{T}$. But, we can manipulate this equation if we apply some different parameters.

Remember, $\Delta U=\Delta Q-P\Delta V$. But what if our system has a constant volume? The pressure-volume work would equal zero. In that case, the change in internal energy equals the change in heat. So, $C_{v}=\frac{\Delta Q}{\Delta T}$.

What about a system under constant pressure? In that case, we still have pressure-volume work. So, we have to define a new term for heat. We call it enthalpy ($H$). The enthalpy is the heat energy transferred in a constant pressure system. We mathematically define the change in enthalpy as $\Delta H=\Delta U+P\Delta V$. But let's expand the equation. We know that $\Delta U=\Delta Q-P\Delta V$. So, our equation becomes $\Delta H=\Delta Q-P\Delta V+P\Delta V=\Delta Q$. How does this relate to the heat capacity? At constant pressure, $C_{p}=\frac{\Delta H}{\Delta T}$. In later lessons, we'll learn many different ways to calculate the enthalpy change.