Knight: Chapter 18
The Micro/Macro Connection(Thermal Energy & Specific Heat, Thermal
Interactions and Heat)
A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C.
Which statement describes the average translational kinetic energies of the molecules?
1. єavg of H2 < єavg of N2.
2. єavg of H2 = єavg of N2.
3. єavg of H2 > єavg of N2.
Quiz Question 1
A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C.
Which statement describes their rms speeds?
1. vrms of H2 < vrms of N2.
2. vrms of H2 = vrms of N2.
3. vrms of H2 > vrms of N2.
Quiz Question 2
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:
Thermal Energy of a Monatomic Gas..
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.
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…
The Equipartition Theorem…
A mass on a spring oscillates back and forth on a frictionless surface. How many degrees of freedom does this system have?
1. 1.2. 2.3. 3.4. 4.5. 6.
Quiz Question 3
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…
Thermal Energy of a Solid…
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
Thermal Energy of a Diatomic Gas…
Systems A and B are both monatomic gases. At this instant,
1. TA > TB.
2. TA = TB.
3. TA < TB.
4. There’s not enough info to compare their temps.
Quiz Question 4