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

The pressure of the gas also increases by a factor of `4`.

Explanation:

Since there is constant volume, we can use Gay-Lussac's Law:

`P_1/T_1 = P_2/T_2`

The problem tells us that the temperature of the gas is increased by a factor of 4. So, we can make the substitution:

`T_2 = 4T_1`

Now, use this substitution to find `P_2` in terms of `P_1`.

`P_1/T_1 = P_2/T_2`

`P_1/T_1 = P_2/(4T_1) color(white)"XXXX"` substitute `4T_1` for `T_2`

`4P_1 = P_2 color(white)"XXXXX"` multiply both sides by `4T_1`

This means that `P_2` is `4` times `P_1`, so we can say that when the temperature of a gas increases by a factor of `4`, the pressure of the gas also increases by a factor of `4`.

Final Answer