In which of the following gas laws is it valid to state temperature in degrees Celsius? A) Charles’ law, B) Boyle’s law, C) The combined gas law, D) Guy-Lussac’s law, or E) The ideal gas law.
Before we try to figure out which gas law it would be valid to state the temperature in Celsius, let’s try to figure out why it wouldn’t be valid to state the temperature in Celsius first. Temperature is ultimately a measure of the average kinetic energy of the particles that are in our system. And the average kinetic energy tells us how quickly the particles in our system are moving around. If our system is a gas that has a high kinetic energy, the gas particles will be moving very quickly. But if our system is a gas with a low kinetic energy, the particles will be moving more slowly.
There are a number of different temperature scales that we use to measure temperature. Celsius and Fahrenheit are relative temperature scales. Celsius and Fahrenheit are relative scales because we’ve defined them relative to things that we can observe. Celsius, for instance, is defined so that zero is when water freezes, and 100 is when water boils.
Kelvin, on the other hand, is not a relative temperature scale. It’s an absolute temperature scale. The kelvin temperature scale is defined so that at zero kelvin, particles have zero kinetic energy. Zero kelvin is sometimes called absolute zero because it’s impossible for things to be colder than that because they can’t have less than zero kinetic energy.
When gas laws refer to the temperature, what it’s really trying to get at is this relationship between the temperature and the average kinetic energy of the gas particles. Which tells us how quickly the gas particles are moving. Since the kelvin temperature scale was defined in reference to the average kinetic energy, all gas laws that refer to the temperature will use the kelvin temperature scale.
So, it would only be valid to state the temperature in degrees Celsius for a gas law if the gas law wasn’t referencing the relationship between the temperature and another variable. This is because, as we’ve said, if the gas law is about the relationship between temperature and another variable, what we’re really talking about is the average kinetic energy of the gas particles. So, we need to talk about that temperature in degrees kelvin.
So with this in mind, let’s look through the gas laws in the answer choices to figure out which one doesn’t include a relationship between temperature and another variable. Charles’ law tells us that for a sample of gas at constant pressure, the volume of the gas is proportional to its temperature. This temperature would, of course, be the absolute temperature. So, answer choice A is not correct. We could not use degrees Celsius in Charles’ law. We would need to use degrees kelvin.
Boyle’s law tells us that for a sample of gas at a constant temperature, the pressure will be inversely proportional to the volume. In Boyle’s law, the temperature isn’t being related to another variable. It’s a constant. So, it would be valid to state the temperature of Boyle’s law in degrees Celsius. So, this is the correct answer choice. But let’s look through the other ones just so we understand them.
Guy-Lussac’s law tells us that for a sample of an ideal gas at a constant volume, the pressure of the gas is proportional to its absolute temperature. Again, this temperature would have to be in kelvin since that’s an absolute temperature scale and Celsius is not.
The combined gas law combines Charles’ law, Boyle’s law, and Guy-Lussac’s law into one law that says the pressure times the volume divided by the temperature is equal to a constant. Again, the temperature scale in the combined gas law is the absolute temperature scale not a relative temperature scale.
Finally, the ideal gas law says that the pressure times the volume is equal to the amount of the gas in moles times the gas constant times the temperature. Like the other gas laws, this temperature must be an absolute temperature. Boyle’s law again is the only gas law where the temperature is held constant. So, it’s the only one where it would be valid to state the temperature in degrees Celsius.