# How much force is required to compress air?

How much force (Newtons) is required to compress normal air in a chamber to 2 atm? For example, if I had a sealed piston pump, how much force would need to be exerted in order for the air to be compressed to 2 atm?

Also, a side note, if I were to compress air from 1 atm to 2 atm, would this have the total volume?

• The force is not a critical physical quantity in this process. You could use even a tiny force if you have the right machine to amplify it. It depends a lot on how and how fast you do the compression. Mar 28 '14 at 7:51
• Even ignoring amplification, pressure is a force per area. The area is totally unspecified here. Mar 28 '14 at 9:54
• Sorry, not a physicist, just curious about the process. As Ruben said, is the the area you mention the surface area in the chamber? Mar 28 '14 at 17:03

## 2 Answers

The state from $1\text{ atm}$ to $2\text{ atm}$ is normally called decompression or contraction. An equation you can use going from one state to the next is: $$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$ Where $P$ is pressure, $V$ is volume and $T$ is temperature. Now if you want to calculate the force you have to know the surface area of what you are (de)compressing. The equation relating force and pressure is: $P=F/A$, where $A$ is surface area.

Finally, keep in mind that you probably have to take into account outside pressure as well, because this has a substantial influence.

To compress the air inside the cylinder of the pump, the force to outside of the cylinder needs to balance the force from the pressure of 2 atm inside. There is the outside air pressure of 1atm, so we need to add force to make up for another 1atm of gas pressure. So the force needed equals the pressure of 1atm (force per area) times the area of the piston.