# Question #9b9c9

Jan 6, 2016

Pressure is directly proportional to temperature if volume, and amount remain constant (Gay-Lussac Law).

#### Explanation:

Consider, for a moment, the ideal gas equation:

$\text{pV}$ $=$ $\text{nRT}$

Now, let's play around with this equation to see what happens. Well, what would happen to the right side of the equation if I were to increase pressure on the left hand side? The value of the left hand side would increase and, since this is an equation, the right hand side must increase in value by an equal amount.

Since $\text{R}$ is the gas constant, the only two quantities on the right hand side of the equation that could change are amount ($\text{n}$) and temperature ($\text{T}$). Thus, if amount is constant, the change in value is entirely due to an increase in temperature. In short, if pressure increases, temperature must also increase proportionately.

In other words:

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature.

Of course, the analogy I used here is comparable to the reverse scenario of changing temperature, and also to decreasing pressure.