Pressure from bouncing molecules

Science · Matter & Materials · ages 16-18

Name ______________________ Date ____________

An elastic collision between two ideal-gas particles can transfer kinetic energy from one particle to the other.
Circle one: True False
In the kinetic model, what directly produces pressure on a gas container's walls?
- Momentum transfer in particle-wall collisions
- Attraction to the walls
- Gravity concentrating all the gas particles on the floor
For an ideal gas in equilibrium, which quantity is directly proportional to kelvin temperature?
- Mean particle mass
- Mean translational kinetic energy per particle
- Mean particle volume in a sample of a single gas
Heating a fixed amount of ideal gas in a sealed, rigid container raises its equilibrium pressure.
Circle one: True False
Ideal-gas samples A and B have the same temperature. B contains twice as many particles as A. How does B's total translational kinetic energy compare with A's?
- The same total energy as sample A
- Twice the total energy in sample A
- Half the total energy in sample A
- Four times the total energy in sample A
Why is mean velocity zero in the rest frame of an equilibrium gas with no bulk flow?
- Opposite velocity directions balance in the average
- Every particle is stationary
- Wall collisions permanently remove all motion from gas particles
An ideal gas is at 300 K. Use k = 1.38e-23 J/K and mean translational KE = 1.5kT. What is its mean translational kinetic energy per particle, in joules?
Answer: ______________
Four sample particles have speeds of 100, 100, 700 and 700 m/s. Calculate their root mean square speed, in m/s.
Answer: ______________
Two ideal gases have different particle masses but the same equilibrium temperature. Which rms-speed comparison is correct?
- Both gases have exactly the same root mean square speed
- Heavier particles have a higher rms speed
- Lighter particles have a higher rms speed
A real gas is compressed to very high density. Why can its pressure differ from the ideal-gas prediction?
- Compression makes all collisions with container walls inelastic
- Compression removes all translational motion from gas particles
- Particle size and interparticle forces affect pressure

Answer key

For grown-ups. Fold this page away before handing over the rest.

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True · An elastic collision conserves the pair's total kinetic energy. Each particle's individual kinetic energy can change.
Momentum transfer in particle-wall collisions · Wall collisions transfer momentum and exert force. Pressure is the average perpendicular force divided by wall area.
Mean translational kinetic energy per particle · Mean translational kinetic energy per particle is 3kT/2. Since k is constant, this energy is proportional to T.
True · Amount and volume stay fixed. Higher typical speeds increase wall-collision frequency and average momentum transfer per collision, raising pressure.
Twice the total energy in sample A · Both samples have the same mean translational energy per particle. B has twice the particles, so it has twice A's total translational energy.
Opposite velocity directions balance in the average · Velocity includes direction. Opposite directions balance in the equilibrium distribution. Particles still move; finite samples can fluctuate around zero.
6.21e-21 · 1.5 x 1.38e-23 x 300 = 6.21e-21 J per particle. Enter 6.21e-21.
500 · Mean squared speed = (10000 + 10000 + 490000 + 490000)/4 = 250000 m^2/s^2. Its square root is 500 m/s.
Lighter particles have a higher rms speed · Equal temperature gives equal mean translational energy per particle. Since this is m v_rms^2/2, lower mass requires higher rms speed.
Particle size and interparticle forces affect pressure · At high density, finite particle size and interparticle forces may no longer be negligible. The ideal model leaves these effects out.