Pressure Law Calculations

The pressure law states that for a fixed mass of gas at constant volume:

$\frac{p_1}{T_1} = \frac{p_2}{T_2}$

Pressure is directly proportional to absolute temperature: $p \propto T$ (temperature MUST be in kelvin).

Graph shapes

• $p$ vs $T$ (in kelvin): a straight line through the origin.
• $p$ vs $\theta$ (in $^\circ$C): a straight line that does NOT pass through the origin (it crosses the temperature axis at $-273$ $^\circ$C).

Worked example

A sealed gas cylinder has a pressure of 200 kPa at 27 $^\circ$C. It is heated to 127 $^\circ$C. Find the new pressure.

Convert to kelvin: $T_1 = 27 + 273 = 300$ K; $T_2 = 127 + 273 = 400$ K.

$\frac{200}{300} = \frac{p_2}{400}$

$p_2 = \frac{200 \times 400}{300} = 266.7 \text{ kPa}$

Why this works (kinetic theory)

Higher temperature means particles move faster. They hit the walls harder (greater momentum change) and more often. Since volume is constant, the area of the walls does not change, so the pressure increases.

Common errors and how to correct them

• Using Celsius instead of kelvin. This mistake costs marks regularly. Always convert to kelvin first.
• Applying this law when the volume changes. Use the combined gas law if both volume and temperature change.

How to apply this in an exam

Convert all temperatures to kelvin. Write $p_1/T_1 = p_2/T_2$. Substitute and solve. Check: if temperature increased, pressure should have increased.