14: Simple Models of Matter

Question 1

Where is thermal energy always transferred?

Answer 1

From regions of higher temperature to regions of lower temperature

Question 2

A change in temperature shows thermal energy has been [ ]

Answer 2

Transferred

Question 3

What does a net transfer of thermal energy cause?

Answer 3

A change in temperature

Question 4

What is specific thermal capacity?

Answer 4

The amount of energy needed to raise the temperature of 1 kg of the substance by 1K

Question 5

What is the set up to measure specific thermal capacity of a solid?

Answer 5

Put a digital thermometer in a hole in your solid
Surround your solid with insulating material
Put an electric heater in another hole in your solid

Question 6

What is the set up for liquids, in order to find the specific thermal capacity?

Answer 6

Have a heating coil inside a beaker of your liquid with a digital thermometer in the beaker surrounded by insulating material and an insulating lid

Question 7

Why is the value you get for specific thermal capacity usually too high in experiments? How can you improve this?

Answer 7

Some of the energy from the heater will get transferred to the air and the container. To minimise this affect, start below and finish above room temperature to cancel out gains and losses. Some energy will also be lost due to resistance in the circuit

Question 8

Describe the experiment to find specific thermal capacity

Answer 8

Heat the substance with the heater so that its temperature increases by about 10 K
Attach an ammeter and voltmeter to your electric heater. You can then calculate the work done by the heater
If you assume all of the work done by the heat is transferred into thermal energy energy in the solid or liquid, you can then plug your data into E = mcΔθ

Question 9

What is an ideal gas?

Answer 9

A model, based on a set of assumptions
An ideal gas is a good approximation of a real gas as long as the pressure isn’t too great and the temperature is reasonably high, compared with the gas’s boiling point

Question 10

What does Boyle’s Law state?

Answer 10

At a constant temperature, the pressure p and the volume V of a gas are inversely proportional

Question 11

Do ideal gases always obey the three gas laws?

Answer 11

Yes

Question 12

Describe what difference temperature makes to a line on the pressure volume graph

Answer 12

The higher the temperature of the gas, the further the curve is from the origin

Question 13

How can you investigate the effects of pressure on volume?

Answer 13

The oil confines a parcel of air in a sealed tube with fixed dimensions. A tyre pump is used to increase the pressure in the tube and the Bourdon gauge records the pressure. As the pressure increases the air will compress on the volume occupied by air in the tube will reduce.
Measure the volume of air when the system is that atmospheric pressure, then gradually increase the pressure, noting down both the pressure and the volume of air. Multiplying them together at any point you should give a constant

Question 14

What does Charles’ law state?

Answer 14

At constant pressure, the volume of the gas is directly proportional to its absolute temperature

Question 15

What does the graph of pressure against temperature look like for an ideal gas?

Answer 15

A straight line, intersecting the X axis at -273.15 Celsius, with a positive gradient

Question 16

Describe the set up for the investigation of the pressure law

Answer 16

Put a flask with a stopper on the top and a beaker of water with a thermometer also in the beaker. The stopper in the top of the flask should be connected by tube to a Bourdon gauge
The volume of the tubing must be much smaller than the volume of the flask.
Make sure as much of the flask is submerged as possible

Question 17

Describe the investigation of the pressure law

Answer 17

Record the temperature of the water and the pressure on the gauge.
Heat the water for a few minutes then remove the heat source, stir the water to ensure it is at her uniform temperature and allow some time for the heat to be transferred from the water to the air. Record the pressure on the gauge and the temperature, then heat the water again and repeat until the water boils. Repeat your experiment twice more with fresh cold water, taking pressure measurements at the same set of temperatures each time.
Plot your results on a graph of pressure against temperature. Draw a line of best fit.

Question 18

What else can you find in the investigation of the pressure law?

Answer 18

This experiment also allows you to estimate the value of absolute zero, again by extrapolating your line of best fit until it reaches the x-axis

Question 19

What equation do you get if you combine all three gas laws?

Answer 19

pV/T = constant

Question 20

What conditions must be met, for a gas to obey as an ideal gas?

Answer 20

Low-pressure and fairly high temperatures

Question 21

What is R, in gas equations? k?

Answer 21

R is the gas constant for one mole of gas

k is the gas constant for one gas particle

Question 22

What are some simplifying assumptions that are used in kinetic theory?

Answer 22

Particles occupy a negligible volume compared with the volume of the container
Collisions between particles themselves or at the walls of the container are perfectly elastic, so no energy is lost.
There are negligible forces between particles, except when they collide.
The gas contains a large number of particles to move rapidly and randomly and that the motion of the particle obeys Newton’s laws

Question 23

What do you use to model the movement of the gas particle?

Answer 23

Random walk

Question 24

What does a random walk assume?

Answer 24

Each particle starts in one place, moves N steps in random directions, and ends up somewhere else

Question 25

What is diffusion?

Answer 25

The net movement of particles from an area of higher concentration to an area of low concentration

Question 26

Why does it take a long time for gases to diffuse?

Answer 26

The distance of particle can travel between collisions is usually around 10⁻⁷ m. So to travel 1 m from a starting point, a particle will have had to take 10 million steps.

Question 27

What is Newton’s second law in relation to gas particles?

Answer 27

The force exerted by a particle in a collision is equal to the rate of change of momentum of the particle

Question 28

What does newtons second law mean about the force exerted on the wall depending on the speed of the particle?

Answer 28

If a particle collides with a wall of the container, the faster it is travelling, the more force it exerts on the wall

Question 29

What is the area under the force time graph equal to?

Answer 29

The change in the momentum, or the impulse of the interaction

Question 30

Explain root mean square speed

Answer 30

As the particles in a gas are moving in different directions, if you averaged their velocities you’d get zero
Instead, you take the average of the squared velocities. This quantity is called the mean square speed
The square root of this number gives you the speed of a typical particle, the root mean square speed

Question 31

Explain the basis of understanding of an ideal gas, by thinking about the gas particle in a box
(Deriving the different gas equation)

Answer 31

A cubic box with sides of length, l, containing one particle, Q, of mass, m.
Say particle Q moves horizontally towards the wall A with a velocity u, so it’s momentum is mu. It strikes wall A, exerting a force on the wall, and heads back in the opposite direction

Question 32

State the four main facts, that are used to derive the different gas equation

Answer 32

1) Particle velocity is proportional to the pressure
2) The number of particles, N, is proportional to the pressure
3) The volume of the box is inversely proportional to the pressure
4) Particles travel in random directions at different velocities

Question 33

Explain why the pressure will be greater in a box, if the particle travels faster
(Deriving the different gas equation)

Answer 33

The faster the particles, the larger its momentum, so the greater the impulse of the collision and the larger the force on the wall. The particle will also take less time to travel across the box and back again, and so will hit the walls more often. And as pressure = force/area, the pressure will be greater to

Question 34

Why is the number of particles proportional to the pressure?

Deriving the different gas equation

Answer 34

Imagine you’ve got a whole stream of particles hitting wall A. Each particle exerts a force on the wall as it hits it, so the total force on the wall will be proportional to the number of particles. Pressure = force/area, the pressure is proportional to the number of particles too

Question 35

Explain why the volume of the box is inversely proportional to the pressure
(Deriving the different gas equation)

Answer 35

Imagine you shrink the box. The particles have less distance to travel before they hit a wall, so you’ve increased the number of times the particles hit the walls of the box per second, which increases the total force on the wall. Because the box is now smaller, the area of the wall is smaller. So there is a greater force on a smaller area, meaning the pressure is greater

Question 36

Explain what the consequence of particles travelling in random directions at different velocities
(Deriving the different gas equation)

Answer 36

You can estimate that a third of all the particles are travelling in one dimension at any time, as there are three dimensions. To take account of the different particle velocities, you can use the mean square speed.

Question 37

What is the internal energy of a system equal to?

Answer 37

The sum of the kinetic and potential energy of the particles within a system

Question 38

What is all the internal energy of an ideal gas due to? Why?

Answer 38

Due to the kinetic energy of its particles, there is no potential energy

Question 39

Describe the relationship between internal energy and temperature of an ideal gas. Explain why

Answer 39

Internal energy of an ideal gas is proportional to its absolute temperature.
A rise an absolute temperature increases the kinetic energy of each particle, causing a rise in internal energy