Section 6.2: Thermal Physics

Question 1

What is the internal energy of a body?

Answer 1

The sum of all the kinetic energies and potential energies of all the particles in the body, where the kinetic and potential energies are randomly distributed.

Question 2

What are the two ways a body’s internal energy can be increased?

Answer 2

Do work on the system to transfer energy to it.

Increase the temperature of the system.

Question 3

Why does internal energy change when the state of a substance changes?

Answer 3

Because the potential energy changes while the kinetic remains constant.

Question 4

Why does the temperature of water remain constant while it boils into water vapour?

Answer 4

Because the energy gained through heating is used to break bonds between molecules rather than increase kinetic energy (and therefore temperature).

Question 5

What is the specific heat capacity of a substance?

Answer 5

The amount of energy required to increase the temperature of 1kg of the substance by 1 degree (C or K), without changing its state.

Question 6

What is the specific latent heat of a substance?

Answer 6

The amount of energy required to change the state of 1kg of that substance, without changing its temperature.

Question 7

State Boyle’s law

Answer 7

For a constant temperature, pressure and volume are inversely proportional.

Question 8

State Charles’ law

Answer 8

For a constant pressure, volume is directly proportional to absolute temperature.

Question 9

State the pressure law

Answer 9

For a constant volume, pressure is directly proportional to absolute temperature.

Question 10

What is the formula to find temperature in kelvin?

Answer 10

K = C + 273

Question 11

What temperature is absolute zero?

Answer 11

-273°C (0 K)

Question 12

What are the theoretical properties of a gas at absolute zero?

Answer 12

Its particles have no kinetic energy, and both the volume and pressure of the gas are zero.

Question 13

What is one mole of a substance equal to?

Answer 13

6.02 × 10^23 atoms/molecules of that substance (defined as the Avogadro constant)

Question 14

What is the molar mass of a substance?

Answer 14

The mass, in grams, of one mole of a substance.

Question 15

What is the equation for work done on a gas to change its volume at a constant pressure?

Answer 15

Work done = pΔV

Question 16

What is Brownian motion?

Answer 16

The random motion of larger particles (such as smoke or dust particles) suspended in a fluid caused by collisions with the surrounding particles of the fluid.

Question 17

Explain Boyle’s law in terms of the simple molecular model

Answer 17

If you increase the volume of a fixed mass of gas, its molecules will move further apart so collisions will be less frequent, meaning pressure decreases.

Question 18

Explain Charles’ law in terms of the simple molecular model

Answer 18

Increasing the temperature of a gas increases the kinetic energy of its molecules, meaning they will move more quickly, and since pressure needs to be constant, the molecules need to be further apart and so volume increases.

Question 19

Explain the pressure law in terms of the simple molecular model

Answer 19

Increasing the temperature of a gas increases the kinetic energy of its molecules, meaning they will move more quickly, and since volume needs to be constant, there will be more collisions per second and at higher speeds, so pressure increases.

Question 20

What are the assumptions in the kinetic theory model?

Answer 20

• No intermolecular forces act on particles
• The duration of collisions is negligible compared to the time between collisions
• Particles move completely randomly
• All collisions are perfectly elastic
• Particles obey Newton’s laws
• Particles move in straight lines between collisions

Question 21

What are the first three steps in the derivation of the kinetic theory model equation?

Answer 21

1. Consider a cube with side length L, full of gas molecules. A molecule, mass m, travels towards a wall of the container with a velocity u. Its change of momentum in the collision will be mu - (-mu), which is 2mu.
2. Before this molecule can collide with this particular wall again, it must travel a distance of 2L. This means the time between collisions, t, is defined as follows: t = 2L/u
3. Using those two pieces of information you can find the impulse, which is the rate of change of momentum:

2mu/t = (mu^2)/L

Impulse is equal to force exerted, so pressure can be found by dividing the impulse by the area of a wall (L^2):

P = (mu^2)/(L^3) = (mu^2)/V (since L^3 is equal to volume)

Question 22

What are the last three steps in the derivation of the kinetic theory model equation?

Answer 22

4. Only one molecule of many has been considered so far, so we need to sum all of the individual pressures of each molecule (m multiplied by the sum of all the speeds, divided by the volume)
5. Instead of considering each speed separately, we can use the mean square speed of all the molecules (the mean of all the squared speeds), and multiply it by N, the number of molecules in the gas.
6. Finally, all three dimensions in which the molecules can move need to be considered:
   ___ ____ ____ ____
   c^2 = u^2 + v^2 + w^2.

Since the molecules move randomly the speed in each direction can be assumed to be the same, therefore
____ ____
c^2 = 3 u^2

Then just put this into the equation and rearrange:
____
pV = 1/3 N m c^2 or pV = 1/3 N m (c rms)^2

Question 23

What does an ideal gas following the gas laws perfectly mean in terms of energy?

Answer 23

Since there are no intermolecular forces between gas molecules, and potential energy is associated with intermolecular forces, an ideal gas must have no potential energy, therefore its internal energy is the sum of the kinetic energies of all its particles.