In physics, the equation of state tells us how the main properties of a substance – pressure p, volume V and temperature T – relate to each other.
For a special class of gases called ideal gases, the relationship is very simple:
p × V is directly proportional to T (when the amount of gas, n, is fixed).
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Think of a bunch of tiny, perfectly elastic balls (like a bunch of balloons) moving around in a box.
If you heat them up, they move faster and collide with the walls more often, so the pressure goes up.
If you squeeze the box (reduce V), the balls hit the walls more frequently, again increasing pressure.
The ideal gas law captures this behaviour mathematically:
p × V = n × R × T.
Here R is the universal gas constant, and n is the number of moles of gas.
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The ideal gas equation is usually written as a block of LaTeX for clarity:
\$pV = nRT\$
Where:
Example:
You have 1 mol of an ideal gas at 300 K in a container of 0.5 m³.
What is the pressure?
Using n = 1 mol, T = 300 K, V = 0.5 m³ and R = 8.314 J mol⁻¹ K⁻¹:
\$p = \\frac{nRT}{V} = \\frac{1\\times 8.314\\times 300}{0.5} = 4.99\\times10^{3}\\text{ Pa}\$
So the pressure is about 5 kPa. 📚
• Always write the full equation pV = nRT before manipulating it.
• Check that the units of n and R match the units you want for p and V.
• Remember that T must be in Kelvin – never use Celsius directly.
• If the problem gives temperature in °C, add 273.15 to convert.
• For quick calculations, you can use the convenient value R = 0.0821 L atm mol⁻¹ K⁻¹ if pressure is requested in atmospheres and volume in litres.
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| Constant | Value | Units |
|---|---|---|
| R (SI) | 8.314 | J mol⁻¹ K⁻¹ |
| R (L atm) | 0.0821 | L atm mol⁻¹ K⁻¹ |
| R (kPa L) | 8.314 | kPa L mol⁻¹ K⁻¹ |