# The gas inside of a container exerts "24 Pa" of pressure and is at a temperature of "75 K". If the temperature of the gas changes to "125 K" with no change in the container's volume, what is the new pressure of the gas?

May 22, 2018

$40 P a$

#### Explanation:

the pressure law states that 'the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.'
[source: http://chemistry.bd.psu.edu/jircitano/gases.html]

direct proportion is a form of direct variation, meaning that $P$ and $T$ increase at the same rate.

in direct proportion, they are linked by a constant. since $P \propto T$, $P$ is a constant multiplied by T.

in shorter notation, $P = k T$.

to find the constant here, use the two values of pressure and Kelvin temperature given: $24 P a$ and $75 K$.

if P = kT, then k = P / T.

$\frac{P}{T} = \frac{24}{75} = \frac{8}{25} = 0.32$

$k = 0.32$

using the same constant, we know that for this fixed volume (since the temperature changes with no change in volume),

$P = 0.32 T$.

here, $T$ is $125 K$.

$P$ (in $P a$) $= 0.32 \cdot 125$

$= 40$

the new pressure $P$ is $40 P a$.