Key relationship
p=⅓nm⟨v²⟩=nkBT; ½m⟨v²⟩=3kBT/2.
Physics · Class 11
Link wall impacts to pressure
Molecules transfer momentum when they bounce from a wall. Random isotropic motion makes the pressure depend on the mean squared speed. Temperature measures their average translational kinetic energy, not the speed of each molecule.
Open the interactive experiment →Link wall impacts to pressure
மூலக்கூறுகள் சுவரில் மோதும்போது உந்தத்தை மாற்றி அழுத்தம் தருகின்றன. வெப்பநிலை சராசரி இயக்க ஆற்றலைக் காட்டும்.
Key notes, relationships and model limits
Remember
Molecules transfer momentum when they bounce from a wall. Random isotropic motion makes the pressure depend on the mean squared speed. Temperature measures their average translational kinetic energy, not the speed of each molecule.
Common trap
All molecules do not move at the RMS speed.
Model limits
Ideal dilute gas with random isotropic molecular motion and elastic wall collisions. Molecules have negligible volume and no interaction away from collisions.
What you will learn
Relate molecular assumptions, wall momentum transfer and macroscopic pressure.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
At n=2.5×10²⁵ m⁻³ and T=300 K, p=2.5×10²⁵×1.380649×10⁻²³×300≈103549 Pa.
Why this matters
The model connects link wall impacts to pressure with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At fixed number density, what happens to ideal-gas pressure when kelvin temperature doubles?
- It quadruples
- Pressure doubles
- It halves
Read the explanation
p=nkBT is linear in T at fixed n.
Course connection: Class XI Chapter 12. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.