Knight: Chapter 18

The Micro/Macro Connection(Thermal Energy & Specific Heat, Thermal

Interactions and Heat)

Mean free path..

Pressure in a gas..

Root-mean-square speed..

Average translational KE..

Last time…

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..

The molar specific heat for a monatomic gas is predicted to be…

Thermal Energy of a Monatomic Gas..

The molar specific heat for a monatomic gas is predicted to be…

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…

The molar specific heat for a solid is predicted to be…

Thermal Energy of a Solid..

The molar specific heat for a solid is predicted to be…

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…

The molar specific heat for a diatomic gas is predicted to be…

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

The nitrogen molecule N2 has a bond length of 0.12

nm. Estimate the rotational frequency of N2 at 20°C.

i.e. 18.7: The rotational frequency of a molecule