Calorimetry is the act of measuring changes of energy in a system by measuring the change in heat. Calorimetry is usually done in a bomb calorimeter, which is a device that is designed to maintain constant volume under extreme pressure. The bomb comes from how they're used: a substance is placed inside the calorimetry and ignited, where it quickly explodes and releases heat which is then read by the calorimeter. In most chemistry classes, students study calorimetry using budget calorimeters made of styrofoam cups, colloquially referred to as "coffee-cup calorimetry."
One term we have to define before continuing is the heat capacity or specific heat of a substance, which is the amount of energy required to heat up one gram of the substance by 1°C. This varies from substance to substance and is usually given in units of `"cal"/(g L)`, where `"cal"` is the unit of calories and is equal to `4.184 J`. You may have noticed that this is the unit used on nutrition labels. Funnily enough, the calories on a nutrition label, despite being written as calories, are actually kcal (1000 calories).
The definition of the calorie is based off the heat capacity of water, `(4.184 J)/(g L)`. This is an astonishingly high heat capacity for a natural substance: in fact, water has the highest heat capacity of any known liquid! This is why water functions well for temperature control. For example, when we sweat, we're releasing water from our bodies which can then absorb heat while only increasing in temperature marginally. In bodies of water as large as the ocean, inordinate amounts of energy are required to increase the temperature of the water.
The relationship between heat and temperature is the following:
`q=mCDeltaT`
Where `q` is the change in heat in Joules (`J`), m is the mass in grams (`g`), `C` is the heat capacity in `J/("mol" K)`, and `DeltaT` is the change in temperature.
Chemists like to pronounce this as "q equals mcat." It's pretty fun to say and makes remembering it simple. For fun (and practice), let's do a problem demonstrating how much energy is necessary to heat up the water in a glass of water.
#1. The average glass of water (8 oz) contains 224 g of water. Calculate the amount of energy required to raise the temperature from 30°C to 45°C.
The heat capacity of water is `(4.184 J)/(g K)`. We're given the mass of water and the change in temperature. Notice that the change in temperature is the same whether it's in °C or K. The only thing left is to plug the values in.
`q=mcDeltaT=(224 g)((4.184 J)/(g K))(318°K-303°K)`
Answer: `14060 J`
This is almost the amount of peak energy of a bullet fired from an M16 rifle! Hopefully this helps to illustrate how much energy water requires to heat up.