# What is Specific Heat Capacity?

## Specific Heat Capacity

Hello, and welcome to this Mometrix video on specific heat capacity- a constant that relates heat transfer to changes in temperature.

Temperature is directly related to the average translational kinetic energy of the atoms or molecules in a system- basically, the faster and heavier the particles are, the higher the temperature. The units for temperature are degrees Celsius and Kelvin (remember, 0 degrees Celsius = 273 Kelvin but 1 degree Celcius has the same magnitude as 1 Kelvin). Conversely, heat is measured in Joules and is the energy transferred between systems at different temperatures that are in contact. Because heat is the transfer of energy, it is known as a process quantity.

When heat is absorbed or released by a system, the temperature changes. How much the temperature changes depends on the substance, and specifically, the specific heat capacity of that substance.

Let’s look at an example.

Let’s say we have 47.8 grams of water at 35ºC and we put it on the stove. We turn on the stove and transfer 1000 Joules of heat to our water and the temperature rises to 40ºC. In other words, it took 1000 Joules of heat to raise 47.8 grams of water by 5ºC. That’s kind of a mouthful and seems oddly specific in terms of quantities. This is where specific heat capacity, notated as “c”, comes into play. It’s a standard quantity and is the amount of heat required to raise 1 gram of a substance by 1 degree Celsius.

With some simple division, we can derive the specific heat capacity of water from our hypothetical cup of water.

Specific heat capacity (c) = qmass × ΔT= \(\frac{1000\text{ Joules}}{47.8\text{ g }× 5\text{ K}}=4.184\text{ J/gK}\)

Specific heat capacity, c, is heat energy divided by the quantity: mass times change in temperature. In our example that would be one thousand joules divided by the quantity forty-seven point eight grams times five degrees Kelvin, which equals four point one eight four joules per gram Kelvin.

From this, we know now that it takes 4.184 Joules to raise the temperature of 1 gram of water by 1 degree Celsius – that’s the specific heat capacity of water.

This is really helpful to scientists because once determined, the specific heat capacity can be used to calculate the heat absorbed or released by a system simply by measuring the temperature change and mass. Let’s try that out.

Let’s look at a new cup of water, let’s say a mug of 350 grams that’s boiling. The water starts at 100ºC and cools down to 90ºC. We want to know how much heat was released from the water to the surrounding environment. Since we know the specific heat capacity of water is 4.184 Joules per gram Kelvin, we simply need to rearrange our previous equation to solve for q (the heat released).

q=c × mass × ∆T=4.184 Jg/K × 350 g × -10 K=-14644 J

Remember, heat energy is specific heat capacity times mass times change in temperature. In this example that is four point one eight four joules per gram Kelvin times three hundred and fifty grams times negative ten degrees Kelvin, which is negative fourteen thousand six hundred and forty-four joules.

Since we knew the specific heat capacity of water, calculating the heat released from the system was easy!

Note here that the negative sign simply tells us that the system (the mug of water) released heat to the surrounding system rather than absorbed it.

Now that we’ve defined specific heat capacity and demonstrated how it can be used to calculate the heat transferred from or to a system, let’s look at why the specific heat capacity changes between substances.

For example, the specific heat capacity of ethanol is 2.18 Joules per gram Kelvin, almost half of water. If we have one gram of water and one gram of ethanol both at 0ºC, it would take 4.18 Joules of heat to raise the temperature of water to 1ºC, and only 2.18 Joules for ethanol. The liquids reach the same temperature but require different amounts of heat. Why?

Remember, to increase the temperature, we need to increase the average translational kinetic energy of the molecules (make the molecules move faster). But the internal energy of a substance is more than just the translational kinetic energy, it also includes potential energy from intermolecular interactions. When heat is transferred to a system, it is distributed amongst the kinetic and potential energies.

So, if a system has more potential energy, a smaller proportion of the transferred heat is distributed to the kinetic energy, yielding a smaller increase in temperature. To better understand this concept, let’s look at water and ethanol again.

In water, there is a complex network of hydrogen bonds between the molecules. Those interactions are part of the potential energy and need to be overcome, or broken, to increase the average translational kinetic energy. So, when we heat water, some of that energy is used to break up the hydrogen bonding network instead of increasing the kinetic energy, resulting in a large specific heat capacity. Conversely, in ethanol, there are fewer hydrogen bonds per molecule, or less potential energy, and therefore a larger proportion of the heat transferred is used to increase the average kinetic energy, which results in a smaller specific heat capacity.

Okay, let’s wrap up with a review. First, we reviewed the scientific definitions of temperature and heat and related them using specific heat capacity. Using water as an example, we showed how once we know the specific heat capacity, it is quite easy to determine the heat transferred from or to a system. And finally, we considered from a microscopic view why substances have different specific heat capacities.

Thanks for watching and happy studying!