# Relation between surface area/shape and pressure [closed]

For a shape with a given volume and given gas pressure inside the volume, if the shape is changed to increase the surface area, will the internal gas pressure change?

• Assume it is an ideal gas? – QuIcKmAtHs Dec 29 '17 at 6:36

## 2 Answers

The ideal gas law states that $PV=nRT$. In your example, shape is changed. Since shape is not a variable in this equation, then there would be no change in pressure.

• Even for a non-ideal gas, the pressure wouldn't change (assuming constant temperature). – Chet Miller Dec 29 '17 at 15:34
• Really? Okay. Looks like I learnt something new today :) – QuIcKmAtHs Dec 29 '17 at 15:35
• But I guess one can easily demonstrate this for the ideal gas scenario – QuIcKmAtHs Dec 29 '17 at 15:36
• For any gas, the general equation of state tells us that pressure is a function only of temperature and specific volume. It takes only two inentsive properties to establish the thermodynamic equilibrium state of a constant-composition single phase material. – Chet Miller Dec 29 '17 at 15:39

The answer depends on whether the change in shape that leads to an increase in surface area is such that the volume of the shape changes. If the volume does not change, then the pressure will not change.