# Worksheet: Thermodynamic Temperature and Molecular Speeds

In this worksheet, we will practice calculating the temperature of a gas in Kelvin, given the root-mean-square speed of the particles within it.

**Q5: **

How many times greater is the average translational kinetic energy of a nitrogen molecule at a temperature of 300 K to the gravitational potential energy of a nitrogen molecule-Earth system at the ceiling of a 3.00 m tall room with respect to the same system with the molecule at the floor?

- A
- B
- C
- D
- E

**Q7: **

The isotopes ^{235}U and ^{238}U are chemically identical, differing only in their atomic masses. The difference in the atomic masses of the isotopes makes it possible to separate them due to the difference between the diffusion speeds of UF_{6} gas containing these isotopes.

The molar masses of the ^{235}U and ^{238}U isotopes of UF_{6} are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical root-mean-square speeds?

At what temperature would the root-mean-square speeds of the ^{235}U and ^{238}U isotopes of UF_{6} differ by 1.00 m/s?

**Q10: **

Nuclear fusion can occur when appropriate nuclei are brought very close together. The mutual Coulomb repulsion of the nuclei must be overcome to bring nuclei sufficiently near each other for fusion to occur. Nuclei can be brought to very small separations using the kinetic energy of high-temperature gas ions or by accelerating nuclei toward one another.

Calculate the potential energy of two nuclei separated by a distance of m. Each nucleus has the same charge as a proton.

- A J
- B J
- C J
- D J
- E J

At what temperature will atoms in a gas have an average kinetic energy equal to the potential energy of two protons separated by a distance of m?

- A K
- B K
- C K
- D K
- E K

**Q11: **

Temperature varies greatly at different parts of the Sun. A location on the Sun’s surface has a temperature of and a location in a region of the Sun’s core has a temperature of .

What is the average kinetic energy of helium atoms at the location on the Sun’s surface?

- A J
- B J
- C J
- D J
- E J

What is the average kinetic energy of helium atoms at the location in the region of the Sun’s core?

- A J
- B J
- C J
- D J
- E J

**Q12: **

The product of the pressure and volume of a sample of hydrogen gas at is 80.0 J.

How many moles of hydrogen are present?

- A0.0320 mol
- B0.0288 mol
- C0.0325 mol
- D0.0433 mol
- E0.0395 mol

What is the average translational kinetic energy of the hydrogen molecules?

- A J
- B J
- C J
- D J
- E J

What is the value of the product of pressure and volume at ?

**Q14: **

A bullet of mass 12 g is traveling horizontally at 350 m/s when it strikes and embeds in a pendulum bob of mass 4.2 kg.

How much mechanical energy is dissipated in the collision?

Assuming that the value of the molar heat capacity at constant volume for the bob plus the bullet is , calculate the temperature increase of the system due to the collision. Take the molecular mass of the system to be 220 g/mol.

**Q15: **

A person is in a closed racquetball court that has a volume of
435 m^{3}. The person is
hitting a ball that has a mass of
52.5 g in random directions
around the room. The ball always collides elastically with the surfaces of the court and
returns to the person who then immediately hits it again. The average kinetic energy of
the ball during this process is
3.20 J.

During the ball’s motion, the velocity of the ball varies. Determine the average value of .

Determine the average pressure on the surface of the racquetball court due to the impacts of the racquetball.

- A Pa
- B Pa
- C Pa
- D Pa
- E Pa