1. Knight: Chapter 18 The Micro/Macro Connection
(Thermal Energy & Specific Heat, Thermal Interactions and Heat)

2. Last time… Mean free path.. Pressure in a gas..
Root-mean-square speed..
Average translational KE..

3. Quiz Question 1
A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C.
Which statement describes the average translational kinetic energies of the molecules?
єavg of H2 < єavg of N2.
єavg of H2 = єavg of N2.
єavg of H2 > єavg of N2.

4. Quiz Question 2
A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C.
Which statement describes their rms speeds?
vrms of H2 < vrms of N2.
vrms of H2 = vrms of N2.
vrms of H2 > vrms of N2.

5. Thermal Energy of a Monatomic Gas..
The thermal energy of a system is Eth = Kmicro + Umicro.
The atoms in a monatomic gas have no molecular bonds with their neighbors, hence Umicro = 0.
Since the average kinetic energy of a single atom in an ideal gas is єavg = 3/2 kBT..
The total thermal energy is:

6. Thermal Energy of a Monatomic Gas..
The molar specific heat for a monatomic gas is predicted to be…

7. Thermal Energy of a Monatomic Gas..
The molar specific heat for a monatomic gas is predicted to be…

8. The Equipartition Theorem…
Atoms in a monatomic gas carry energy exclusively as translational K..
can be thought of as independent modes of storing energy (a.k.a. 3 degrees of freedom (d.o.f)).
Notice:
Molecules in a gas may have additional modes of energy storage, i.e. the K and U associated with vibration, or rotational K.

9. The Equipartition Theorem…
The thermal energy of a system of particles is equally divided among all the possible degrees of freedom.
For a system of N particles at temperature T, the energy stored in each mode is…

10. Quiz Question 3
A mass on a spring oscillates back and forth on a frictionless surface.
How many degrees of freedom does this system have? 1. 2. 3. 4. 6.

11. Thermal Energy of a Solid…
Model a solid as atoms connected by spring-like molecular bonds…
3 d.o.f. associated with K
3 d.o.f. associated with U
6 d.o.f. total.
The energy stored in each d.o.f. is ½ NkBT…

12. Thermal Energy of a Solid..
The molar specific heat for a solid is predicted to be…

13. Thermal Energy of a Solid..
The molar specific heat for a solid is predicted to be…

14. Thermal Energy of a Diatomic Gas…
Model a diatomic molecule as atoms connected by spring-like molecular bonds…
3 d.o.f. associated with translational K
2 d.o.f. associated with rotational K
5 d.o.f. total*
The energy stored in each d.o.f. is ½ NkBT…
* at commonly used temps

15. Thermal Energy of a Diatomic Gas..
The molar specific heat for a diatomic gas is predicted to be…

16. Quiz Question 4
Systems A and B are both monatomic gases. At this instant,
TA > TB.
TA = TB.
TA < TB.
There’s not enough info to compare their temps.

17. i.e. 18.7: The rotational frequency of a molecule
The nitrogen molecule N2 has a bond length of 0.12 nm. Estimate the rotational frequency of N2 at 20°C.