Which of the following formulas most correctly represents the relation between the pressure, volume, and absolute temperature of an ideal gas? A) Pressure times volume is proportional to temperature. B) Volume divided by pressure is proportional to temperature. C) Pressure divided by volume is proportional to temperature. D) Volume divided by temperature is proportional to pressure. E) Pressure divided by temperature is proportional to volume.
Among these answer choices, we see just about every arrangement of these three variables. We want to choose which one is correct. And we’re helped in the fact that the kind of gas we’re working with is an ideal gas. This tells us that we can refer to the ideal gas equation for guidance on the relationship between pressure, volume, and absolute temperature.
The ideal gas equation is often written this way. It says that the pressure of this gas multiplied by its volume is equal to the number of moles of gas multiplied by a gas constant, capital 𝑅, all times the absolute temperature of the gas 𝑇.
It’s this relationship, the ideal gas law, that reveals the correct relation between pressure, volume, and absolute temperature. Looking again at the ideal gas law, we see that pressure times volume is equal to some constant, the number of moles of gas, times a gas constant times the temperature of the gas.
If 𝑛 times 𝑅 is a constant, and it is, then that means we can rewrite this expression. If we want to, we can combine 𝑛 and 𝑅 into one overarching constant, we’ll call capital 𝐶.
And yet another way to write this is to say that since 𝑃 times 𝑉 is equal to a constant times 𝑇, then that means that 𝑃 times 𝑉 is proportional to the temperature 𝑇. We get this result from our ideal gas law by recognizing that 𝑛 times 𝑅 is a constant value.
So which answer choice does this result indicate? We see we have a match with answer choice A. Pressure times volume is proportional to absolute temperature. This is the correct representation of the relationship between these three variables in an ideal gas.