Why cold solids hold less heat

Science · Matter & Materials · ages 23-24

Name ______________________ Date ____________

A cooled solid keeps heat capacity 3R all the way down.
Circle one: True False
What heat capacity does equipartition predict near room temperature?
- Near zero
- Steady 3R, about 25 joules per mole per kelvin
- Infinite capacity
Where does the energy of a warmed solid live?
- In atomic jiggles of motion plus spring energy
- In nuclear fusion reactions
- Outside the crystal entirely
Capacity follows T cubed. At some T it reads 8 units. What does it read at half that T?
Answer: ______________
Why do most vibrational modes freeze at low temperature?
- kT below packet hf, so empty
- Atoms leave the lattice
- Springs become infinitely stiff
How do the two dispersion branches differ?
- Hot atoms versus cold atoms
- Big atoms versus small atoms
- Neighbours together versus against each other
Ned counts every mode at low temperature and expects 3R. What is wrong?
- Most frozen; only slow ones count
- T-cubed is a misprint
- Acoustic branches vanish when cooled
Why is the classical Dulong-Petit rule a high-temperature limit?
- Crystals melt at high temperature
- Packets look tiny beside kT there
- Springs vanish when warmed

Answer key

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

False · Capacity falls toward zero as modes freeze.
Steady 3R, about 25 joules per mole per kelvin · Six shares per atom give 3R per mole.
In atomic jiggles of motion plus spring energy · Atoms shake around lattice places in all three directions.
1 · Halving gives an eighth: 8 over 8 is 1.
kT below packet hf, so empty · Packets larger than kT cannot be bought.
Neighbours together versus against each other · Acoustic swings together like sound; optical swings against, excitable by light.
Most frozen; only slow ones count · The cutoff census keeps only affordable slow modes.
Packets look tiny beside kT there · Large kT affords every packet, restoring smooth equipartition.