# Pressure change of a gas upon increasing the temperature

My assignment is as follows:

A sample of air is trapped in a container at 16.2 psi. If the initial temperature is increased from 10°C to 32°C, what is the final pressure?

I am really confused as to what psi is and how am I supposed to convert it to figure out the final pressure.

• Psi-pounds of pressure per square inch. For the calculations and a good explanation google the page "pressure increase due to thermal expansion @Eng-tips.com engineering forums. – Technetium Nov 26 '15 at 6:02
• The ideal gas law - PV=NRT=mRT should be able to be used here. – Technetium Nov 26 '15 at 9:11
• Strictly speaking, you don't even need to know what psi is. Just apply the ideal gas law and return your answer in the same units. – Ivan Neretin Dec 1 '16 at 9:21
• Be careful here, the constant R has many values, some of which works with psi. But yea, apply ideal gas law with the appropriate R and you don't need to concern yourself with psi. R is approximately 5.961 ft3 psi K^-1 lb-mol^-1 – Stian Yttervik Dec 1 '16 at 12:16

In the given experiment, there is no indication that the volume of the container changes and/or a reaction takes place. Both the volume and the number of moles can therefore assumed to be constant.

Let's assume that the enclosed air can be treated as an ideal gas.

Under these conditions, the pressure is proportional to the absolute temperature (in Kelvin):

$$p \propto T\quad\quad \frac{p_1}{p_2} = \frac{T_1}{T_2}$$

This relation is known as Amonton's Law.

I am really confused as to what psi is and how am I supposed to convert it to figure out the final pressure.

Using the equation above, you would only have to convert the temperatures to Kelvin and could give the final pressure as $\mathrm{psi}$ too.

If you insist on conversion to Pascal ($\mathrm{Pa}$) as your favourite SI unit for pressure, remember that a pressure is defined as a force acting on a surface (area):

$$\mathrm{1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m\,s^2}}$$

The $\mathrm{psi}$ is a still rather common unit and it stands for pounds per square inch.

This double weird, since both the force and the area are expressed in non-SI units.

Note that the pound is not the German Pfund ( = $\mathrm{0.500\,kg}$), but the angloamerican pound with $\mathrm{1\,lb = 0.453\,kg}$.

The area part in $\mathrm{psi}$ is given in square inches with $\mathrm{1\,in = 0.0254\,m}$.

In summary, $\mathrm{1\,psi \approx 6895\,Pa}$.