The gas inside of a container exerts #18 Pa# of pressure and is at a temperature of #360 ^o K#. If the pressure in the container changes to #27 Pa# with no change in the container's volume, what is the new temperature of the gas?
The final temperature,
This question is an example of Gay-Lussac's gas law, which states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. This means that if the pressure increases, so does the temperature, and vice-versa. The equation to use in order to answer your question is:
Organize your data.
Rearrange the equation to isolate
As you can see, as the pressure increased, so did the temperature.
We can use the temperature-pressure relationship of gases illustrated by Gay-Lussac's law:
At constant volume, the temperature and pressure of a fixed quantity of gas are directly proportional to each other, which is explained by the kinetic-molecular theory.
We can rearrange this equation to solve for the final temperature
and finally, plug in the known variables to find the temperature.