How Do You Read a Pressure-Volume Diagram for a Gas?

For IB Physics SL and HL, read a pressure-volume diagram by locating each gas state from its pressure and volume coordinates, then follow the direction of the path to determine how these quantities change. For a fixed amount of ideal gas, use $PV=nRT$ to interpret the corresponding temperature change.

A pressure-volume diagram (or $P$-$V$ diagram) plots pressure on the vertical axis and volume on the horizontal axis. Each point represents an equilibrium state of the gas; a line connecting two points represents a process through which the gas changes state.

Always check axis units and scale. Pressure is commonly given in $\text{Pa}$ or $\text{kPa}$, while volume may be in $\text{m}^3$, $\text{dm}^3$, or litres.

For example, suppose state A has $P=2.0\times10^5\,\text{Pa}$ and $V=0.010\,\text{m}^3$, while state B has and . Since

$$P_AV_A=P_BV_B=2.0\times10^3\,\text{J},$$

the temperature is unchanged if the amount of ideal gas is fixed. The path is therefore isothermal.

A common misconception is that every downward-sloping curve is automatically isothermal. It is isothermal only if $PV$ remains constant.

HL-only extension: In B.4 Thermodynamics, the area under a $P$-$V$ path equals the work done by the gas, $W=\int P\,dV$. This is not required as part of B.3 alone.

In an exam, state the direction of change, identify any constant quantity, and support your conclusion using coordinates or $PV=nRT$. Do not identify a process from the curve's appearance alone.