Squashing a gas at constant temperature, p₁V₁ = p₂V₂, and why doing work on a gas warms it.
What you will learn
- Use pV = constant for a gas at constant temperature
- Explain the change in pressure in terms of particles
- Explain why pumping up a tyre warms the air (Higher)
Squash it, the pressure rises
For a fixed mass of gas at constant temperature:
pressure × volume = constant
p₁ V₁ = p₂ V₂
Halve the volume and the pressure doubles: the same particles hit a smaller area of wall more often. Any units work, as long as both sides use the same ones (kPa and cm³ is fine). To find a new volume: V₂ = p₁ V₁ ÷ p₂.
Pressure is inversely proportional to volume: double one and the other halves. So a graph of pressure against 1 ÷ volume is a straight line through the origin.
- 200 cm³ of air at 100 kPa squashed to 50 cm³
- 100 × 200 = p₂ × 50
- p₂ = 20 000 ÷ 50 = 400 kPa
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- Squash it, the pressure rises
- Doing work on a gas (Higher)
- Try it: p₁V₁ = p₂V₂
9 practice questions, marked as you go; about 20 minutes in all.
Key terms
Inversely proportional
In this unit: Particle model, density and gas pressure
Density and its required practical, changes of state, specific latent heat, and the particle model of gas pressure, including p₁V₁ = p₂V₂.