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

Mar 28, 2017

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:

${T}_{2} = 4 {T}_{1}$

Now, use this substitution to find ${P}_{2}$ in terms of ${P}_{1}$.

${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$

${P}_{1} / {T}_{1} = {P}_{2} / \left(4 {T}_{1}\right) \textcolor{w h i t e}{\text{XXXX}}$ substitute $4 {T}_{1}$ for ${T}_{2}$

$4 {P}_{1} = {P}_{2} \textcolor{w h i t e}{\text{XXXXX}}$ multiply both sides by $4 {T}_{1}$

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 $4$.