Question

The absolute temperature of a gas is increased four times while maintaining a constant volume. What happens to the pressure of the gas?

Answer 1

It also increases by a factor of `4`.

Explanation:

We can use the temperature-pressure relationship of gases, illustrated by Gay-Lussac's law:

`(P_1)/(T_1) = (P_2)/(T_2)`

We're not given any specific values for each quantity, but we can use `1` for the original temperature (`T_1`) and `4` for the final temperature (`T_2`) to illustrate that it increased by a factor of `4`. To find out how the pressure changes, we can rearrange the equation to solve for the final pressure, `P_2`, and plug in the two temperature values to find how the pressure changed (in terms of `P_1`):

`P_2 = (P_1T_2)/(T_1)`

`P_2 = (P_1(4))/(1)`

Therefore,

`P_2 = 4(P_1)`

The pressure increases by a factor of `4`, same as the temperature, which is explained by the kinetic-molecular theory.