Heat capacity and specific heat

Kim and Philip want to make some tea. That’s too much water, Philip! It’s going to take forever to boil! Kim is right. To boil a lot of water requires more time and energy.

Why is that so? When you heat up water, you transfer thermal energy from the cooker to the water. Then, the temperature of the water rises because the particles inside start moving faster. The water takes in thermal energy, which turns into energy of motion - kinetic energy of the particles. In this form the energy is stored inside the water.

The amount of heat a substance can take in and store is its HEAT CAPACITY. Heat capacity depends on three factors: - by how much the temperature changes - how much of a substance there is - and what substance it is. Higher temperature means higher kinetic energy of atoms. So the more we raise the temperature, the more energy is stored in the substance. The amount of substance matters, because it determines how many particles there are.

Each of the particles inside a substance stores energy, so the more of them, the more energy they can take in and store altogether. Counting particles would be very impractical, so we just use mass to express the amount of substance. To see what type of substance has to do with heat capacity, let’s do an experiment! We start with taking two identical glass beakers. We fill one of them with some water and the other one with the same amount of ethanol.

Let’s place them over the same heat for the same period of time - 60 seconds. Now, if we measure temperature in each pot, will there be any difference? Let’s see... The ethanol is much hotter than water! This is because ethanol and water are made of different molecules, which are connected and arranged in different ways.

In some substances, it is easier for atoms to move - the kinetic energy increases faster, and so does the temperature. Other substances, like water, will need to absorb more energy from the outside to make the atoms move. The kinetic energy of atoms will increase slowly, and so will temperature. The amount of heat it takes to raise the temperature of one kilogram of a substance by one degree Celsius or one kelvin is specific for that substance. We call this property SPECIFIC HEAT CAPACITY - or just SPECIFIC HEAT.

Substances with high specific heat, like water, can take in and store more heat than those with lower specific heat - like ethanol. For many substances, we can look up the value of specific heat in a table. But what if we have an object and we don’t know what substance it’s made of - like this metal ball? We can’t find its specific heat in the table - but we can calculate it ourselves! We know it weighs half a kilogram, and to heat it up by 50 kelvins we need 3250 units of energy - joules.

We can take this data and put it into a formula: Energy - 3250 joules divided by mass - half a kilogram, and the temperature difference - 50 kelvins. We get the result - the specific heat of this metal is equal to 130 joules per kilogram kelvin Hm, if the specific heat of water is approximately 4200 joules per kilogram kelvin, can you tell what heats up more easily - half a kilogram of water or this metal ball…?