Problem
You want to study experimentally the pressure-temperature dependence of a gas at constant volume. For each element state whether it is a controlled, independent, or dependent variable: the volume of the container, the number of moles, the type of gas, the temperature, the pressure.
Solution
In an experiment we distinguish three roles for the quantities:
- independent variable: the one the observer deliberately varies;
- dependent variable: the one that is measured and responds to variations of the first;
- controlled variables: those kept fixed so they do not affect the relationship being studied.
Let’s analyse each element:
- Volume of the container: by construction of the experiment, this is kept constant. It is therefore a controlled variable.
- Number of moles: the amount of gas must not change during the trial, otherwise it would distort the relationship. It is a controlled variable.
- Type of gas: the same gas is always used; changing it would introduce an extra variable. It is a controlled variable.
- Temperature: this is the quantity we choose to vary in order to observe its effect. It is the independent variable.
- Pressure: this is what we read on the instrument in response to the imposed temperature. It is the dependent variable.
Since the volume, number of moles, and type of gas remain fixed, the experiment isolates exactly the relationship between pressure and temperature, which is Gay-Lussac’s law: at constant volume the pressure is proportional to the absolute temperature,