5.1

Question 1

Explain what is meant by thermal equilibrium?

Answer 1

Two bodies in thermal equilibrium have the same temperature and no net flow of thermal energy between them.

Question 2

Explain how to convert degrees Celsius into kelvin.

Answer 2

Temperature in K=Temperature in °C+273 °C

Question 3

Explain the difference between temperature and heat.

Answer 3

Temperature is a measure of the hotness of a substance, it is measured in °C or K. Heat is a measure of the thermal energy of a substance, it is measured in joules.

Question 4

What direction is the energy transfer?

Answer 4

High heat to low heat.

Question 5

Define the triple point of water.

Answer 5

The triple point of water is defined as the temperature and pressure at which the three states of water (ice, water and steam) can exist at equilibrium. This is 273.16 K and 0.61 kPa.

Question 6

Explain why the ‘absolute scale of temperature’ has this name.

Answer 6

The absolute scale of temperature, the kelvin, is not defined using the properties of any substance. It is defined using absolute zero – the lowest possible temperature which exists when a system has minimum energy.

Question 7

Explain the importance of water in the Celsius scale of temperature.

Answer 7

The Celsius scale is defined by two fixed points – both of which use the properties of water:
The steam point – This is 100 °C. This is the temperature at which steam and liquid water are in
equilibrium at standard atmospheric pressure.
The ice point – This is 0 °C. This is the temperature at which ice and liquid water are in equilibrium at
standard atmospheric pressure

Question 8

Convert 96 °C into kelvin.

Answer 8

Temperature in kelvin = 96 + 273 Temperature in kelvin = 369 K

Question 9

Convert 203 K into Celsius.

Answer 9

Temperature in Celsius = 203 − 273 Temperature in Celsius = -70 °C

Question 10

Convert 150 °C into K.

Answer 10

Temperature in kelvin = 150 + 273 Temperature in kelvin = 423 K

Question 11

Compare solids, liquids and gases in terms of their spacing, order and motion.
Include a diagram in your answer.

Answer 11

Solids

The molecules are close to each other and vibrate around fixed positions in a random way. The molecules are regularly arranged in a 3D lattice structure. There are strong electrostatic attractions between molecules.

Liquids

The molecules are now free to move randomly but they are still in contact with other molecules and vibrating. There is only a weak attraction between the molecules.

Gases

The molecules are no longer in contact and move rapidly and randomly. The attraction between the molecules is negligible.

Question 12

Define internal energy.

Answer 12

Internal energy is the sum of the random distribution of kinetic and potential energies associated with the molecules of a system.

Question 13

Describe and explain what happens to the internal energy of a substance as the temperature decreases.

Answer 13

The internal energy will decrease. As the temperature decreases the particles vibrate less; this decreases the kinetic energy. As the internal energy is the sum of the kinetic and potential energies in a system, this decrease in kinetic energy decreases the internal energy.
Internal energy will not decrease to zero as electrostatic potential energy will always be stored in the particles.

Question 14

State two factors that would
change the internal energy of a
system.

Answer 14

• The input or removal of heat energy to or from the system.

- Doing work on the system, or the system doing work on the system.

Question 15

Define absolute zero.

Answer 15

The temperature of a substance which has a minimum amount of internal energy.

Question 16

During a change in state from
gas to liquid explain what
happens to:

a) the temperature
b) the potential energy
c) the internal energy

Answer 16

a) The temperature stays constant. This is because all of the energy being removed from the system is being used to form forces of attraction between the gas molecules to change its state to liquid.
b) The potential energy decreases as the molecules are forming bonds and coming closer to each other.
c) The internal energy decreases. This is because the kinetic energy stays constant and the potential energy decreases. Internal energy is the sum of the potential and kinetic energies in a system.

Question 17

Describe Brownian motion, giving an example of it.

Answer 17

Brownian motion is the continuous random motion of small particles suspended in a fluid, visible under a microscope.

An example that shows Brownian motion is the motion of smoke particles in air or pollen grains in water.

Question 18

Describe what Brownian motion tells us about air molecules.

Answer 18

Air molecules are:

• small (compared to smoke particles)
• moving randomly
• moving rapidly

Question 19

Explain what causes Brownian motion.

Answer 19

Brownian motion is caused by the collisions of small particles with the particles of the fluid that contains them. These collisions are rapid, random and occur in all directions.
The net force on the particle determines the direction of motion of the particle.
At any given moment this net force may be in a different direction; this leads to the zigzag motion of the particles.

Question 20

Define the specific heat capacity.

Answer 20

The energy required to change the temperature of 1 kg of a substance by 1 K (or 1 °C).

Question 21

State an equation for the specific heat capacity.

State what each of the terms means.

Answer 21

E = mc∆θ

E − thermal energy
m − mass
c − specific heat capacity
∆θ − temperature change

Question 22

Derive the units of specific heat

capacity.

Answer 22

E = mc∆θ

c =E/m∆θ
c =J/kg × K
c = Jkg^−1K^−1

Or
c = Jkg^-1°C^-1

Question 23

An object is heated up.

State three factors that the object’s temperature rise will depend on.

Answer 23

The material that the object is made of / the material’s specific heat capacity.
The mass of the object.
The thermal energy supplied to the object.

Question 24

Define specific latent heat of fusion.

Answer 24

The specific latent heat of fusion is the energy required to change 1 kg of a solid into a liquid at constant temperature.

Question 25

Define specific latent heat of vaporisation.

Answer 25

The specific latent heat of vaporisation is the energy required to change 1 kg of a liquid into a gas at constant temperature.

Question 26

State an equation for specific latent heat.

Answer 26

E = mL E − energy transferred m − mass L − specific latent heat

Question 27

Describe an electrical experiment to measure the specific heat capacity of a substance. State the apparatus needed, and the equations required to calculate the specific heat capacity.

Answer 27

- Measure the mass of the substance using a balance. - Put an electrical heater into the substance. - Put a thermometer into the substance. - Connect a voltmeter and ammeter to the circuit containing the electrical heater. - Measure the temperature of the substance before heating. - Switch on the electrical heater. - Use a stopwatch to measure the heating time. - Turn off the electrical heater. - Measure the temperature of the substance after heating. Use these equations to calculate the specific heat capacity: Q = IVt - If there are no energy losses: IVt = mcΔθ - Therefore, we can find the specific heat capacity using: c =IVt/mΔθ

Question 28

Calculate the energy required to increase the temperature of 7 kg of water from 20 °C to 90 °C. The specific heat capacity of water is 4200 J kg^–1 K^–1.

Answer 28

Q = mcΔθ Q = 7 × 4200 × 70 = 2 058 000 J The energy required is 2 058 000 J.

Question 29

Give an example of a time when the high heat capacity of water is an important property.

Answer 29

The body – 70% water content of the body ensures that the body remains at a constant temperature. Coolant in power stations – useful in transferring energy. Car radiator – useful in transferring energy.

Question 30

Explain why calculating the specific heat capacity experimentally may give an inaccurate measurement of the specific heat capacity.

Answer 30

- Heat loss to the surroundings - Heat loss to the apparatus - The substance may continue to heat up for a while after you finish timing - The substance may not heat up uniformly

Question 31

Describe an electrical experiment to measure the latent heat of vaporisation of water.

Answer 31

- Put water of a known mass into a double container, the inner container of which contains a small hole. - Submerge an electrical heater. - Connect an ammeter in series and a voltmeter in parallel to the electrical heater. - The electrical heater is turned on and some of the water begins to boil, turning to steam and escaping through the hole. - The water then condenses and is collected in a beaker. - The experiment is carried out over a time t; the time is measured using a stopwatch. - The mass of water evaporated and collected in the beaker is measured using a balance. - The voltage and current are measured using the voltmeter and ammeter. ``` We use the fact that: E = mLv and: E = VIt to say: mLv = VIt Therefore: Lv = VIt/t ```

Question 32

Suggest some possible sources of error that would need to be taken into account when measuring the specific latent heat of fusion and of vaporisation of water.

Answer 32

- The apparatus may heat up, need to take their specific heat capacity into consideration. - The water may continue to change state after the electrical heater is turned off – this can be improved by finishing timing when it stops changing state rather than when the heater is turned off. - The water remaining in the container will have heated up – need to take its specific heat capacity into consideration.

Question 33

Explain the difference between the specific latent heat of fusion and the specific latent heat of vaporisation.

Answer 33

The specific latent heat of fusion is the energy required to change 1 kg of a solid into a liquid, whereas the specific latent heat of vaporisation is the energy required to change 1 kg of a liquid into a gas.

Question 34

2 kg of material X requires 3.2 kJ to change state from a solid to a liquid. Calculate the specific latent heat of fusion of material X.

Answer 34

``` Q = mL L = Q/m = 3200/2 = 1600 J kg −1 ```

Question 35

A 1 kg block of ice of temperature –5 °C was melted and heated to 70 °C. Calculate the energy required. ``` cICE = 2200 J kg−1K−1 cWATER = 4180 J kg−1K−1 LfICE= 334 kJ kg−1 ```

Answer 35

This question has three stages: First find how much energy is needed to increase the temperature of ice from –5 °C to 0 °C. Q = mcΔθ Q = 1 × 2200 × 5 = 11 000 J Now, find how much energy is need to change the state of solid ice to liquid water. Q = mL Q = 1 × 334 000 = 334 000 J Finally, find how much energy is need to increase the temperature of water from 0 °C to 70 °C. Q = mcΔθ Q = 1 × 4180 × 70 = 292 600 J Total energy required: 11 000 + 334 000 + 292 600 = 637 600 J

Question 36

State an equation that links pressure with the mean square speed. State what each of the terms means.

Answer 36

pV =1/3NmCrms^2 ``` p − pressure V − volume N − number of molecules m − mass c2̅ − mean square speed ```

Question 37

Explain what Avogadro’s constant tells us.

Answer 37

Avogadro’s constant tells us that there are 6.02x10^23 particles in one mole of a substance.

Question 38

State an equation to find the number of moles of a known substance given its mass.

Answer 38

n =m/Mr n − number of moles m − mass Mr − molar mass (relative atomic/formula mass)

Question 39

State an equation to find the number of molecules in a substance given the number of moles.

Answer 39

N = nNA N − number of molecules n − number of moles NA − Avogadro′s constant (6 × 1023 mol−1)

Question 40

Show that: pV = NkT

Answer 40

We know that: pV = nRT and that: k =R/NA Combining these two equations: R = kNA pV = nNAkT We also know that: nNA = N Finally: pV = NkT

Question 41

Derive the equation: | 1/2mc̅̅2̅ =3/2kT

Answer 41

We know that: pV = NkT and that: pV =1/3Nmc̅̅2̅ Equating these two equations gives us: NkT =1/3Nmc2̅ Cancel N: kT =1/3mc2̅ Multiply each side by 3/2: 1/2mc̅̅2̅ =3/2kT

Question 42

Explain what is meant by the internal energy of an ideal gas.

Answer 42

The internal energy of an ideal gas is the sum of the mean kinetic energies of all the moleules in the gas. For an ideal gas we assume potential energy is negligible (Ep=0), and so the internal energy is the sum of the mean kinetic energies.

Question 43

State Boyle's law.

Answer 43

For a fixed mass of a gas at a constant temperature, pressure is inversely proportional to volume.

Question 44

What is the graph of P against V, at a constant temperature? What does it look like at a higher temperature?

Answer 44

Inversely proportional. Shift to the right.

Question 45

Define Pressure.

Answer 45

The force exerted per unit area.

Question 46

What causes pressure to be exerted in terms of Newtonian theory?

Answer 46

For a gas in a container, we assume that the gas particles will undergo perfectly elastic collisons with the walls of the container. During the collisions, the particles have a change in momentum. By obeying Newton's second law: F=∆p/∆t This means that the wall has exerted a force on the gas particle to cause this change in momentum. Newton's third law, which states that for every body that exerts a force, a force of equal magnitude and opposite direction is exerted back on that body. Therefore, as the wall of the container exerts a force on the gas particle, the gas particle also exerts a force on the walls of the container. The force causes the pressure experienced on the walls of the container: P= F/A

Question 47

What is meant by the absolute zero of temperature?

Answer 47

The temperature at which the particles have zero kinetic energy. This is the lowest possible temperature as 0 K on the kelvin scale.

Question 48

(Graph showing pV against Temperature, straight line through the origin) What does the gradient tell us?

Answer 48

We know that: pV = nRT This can be compared to: y = mx + c Therefore, gradient(m) = nR

Question 49

A gas ov volume 100cm^3, with constant pressure, expands to a volume of 200cm^3. Given that the final temperature of the gas is 27C, calculate the intial temperature of the gas.

Answer 49

V/T = constant V1/T1 = V2/T2 All temperature must be converted into kelvin and volumes into m^3 100 x 10^-6 / T1 = 200 x 10^-6 / 300 T1 = 150K The initial temperature of the gas was 150K (-123C).

Question 50

A gas has a pressure of 6x10^4 Pa, a temperature of 30C and a volume of o.1m^3. a) calculate the number of molecules in the gas. b) Given that the gas is nitrogen gas N2, calculate the mass of the gas. The molar mass of a nitrogen atom is 0.014kg.

Answer 50

pV = NkT Convert temperatures to kelvin. a) N = pV/kT = (6x10^4x0.1)/(1.38x10^23 x 303) = 1.43 x 10^24 molecules b) to find the number of moles n: ``` n = N/Na == (1.43 x 10^24)/(6.02x10^23) = 2.38 moles n = m/Mr ``` Therefore, m =Mr x n = 0.028 x 2.38 = 0.067 kg

Question 51

A piston contains 0.5 m3 of air at a pressure of 7x104 Pa. | If the piston is compressed, decreasing the volume of air to 0.2 m^3, find the new pressure of the gas in the piston.

Answer 51

pV = constant p1V1 = p2V2 7 × 10^4 × 0.5 = p2 × 0.2 p2 = 1.75 × 10^5 Pa

Question 52

Oxygen atoms have a molar mass of 0.016 kg. a) Calculate the number of molecules in 5 moles of oxygen gas O2. b) Calculate the mass of 5 moles of oxygen gas O2.

Answer 52

a) N = n x NA N = 5 × 6.02 × 10^23 = 3.01 × 10^ 24 b) m = Mr x n m = 0.032 × 5 = 0.16 kg

Question 53

State an equation for the Boltzmann constant.

Answer 53

``` k = R / NA where: k − Boltzmann constant R − gas constant NA − Avogadro's constant ```

Question 54

Explain how an increase in temperature leads to an increase in pressure.

Answer 54

- At higher temperatures, the molecules have more kinetic energy and move faster. - There is a larger change in momentum which causes a larger force. - The molecules have more frequent collisions with the walls of the container. - Pressure is force per unit area so the increase in force means an increase in the pressure.

Question 55

Describe a technique that could be used to demonstrate Boyle’s law.

Answer 55

Use a piston which has air trapped inside. Compress the piston using weights added to the top of the piston. Vary the weights added and record the changes in volume of the gas in the piston. Calculate the pressure using the fact that: pressure = force / area Plot a graph of pressure against 1/volume – the graph will show that the two values are directly proportional. ``` P = constant / V PV = constant ``` Pressure is inversely proportional to volume (i.e. directly proportional to 1/volume).

Question 56

Describe a technique that could be used to demonstrate the pressure–temperature law.

Answer 56

Surround a gas container with water and connect it to a pressure gauge. Increase the temperature of the water and measure the pressure. Do this for a variety of different temperatures. Plot a graph of pressure against temperature. The graph will show that pressure is directly proportional to temperature. Therefore: P/T = constant

Question 57

Describe how a pressure vs temperature graph could be used to determine the value of absolute zero in Celsius.

Answer 57

Plot a graph with pressure on the y-axis and temperature in Celsius on the x-axis. The point at which the line crosses the x-axis will give an approximate value of absolute zero in Celsius. The point at which it crosses x = absolute zero, because absolute zero occurs when P = 0.

Question 58

Explain Boyle’s law in terms of the kinetic theory of gases.

Answer 58

When a gas is at a constant temperature, its pressure can be decreased by increasing its volume. In a larger volume, the molecules of gas will travel further between collisions with the walls on the container. Therefore, there are fewer collisions per second – the pressure is less. The reverse argument could also be given (a smaller volume increases the pressure as there will be more frequent collisions).

Question 59

State five assumptions of an ideal gas.

Answer 59

1. Volume of the molecules is negligibly small compared to the volume of the gas. 2. Molecules have elastic collisions (no energy losses with walls of container). 3. There is a large number of molecules. 4. Molecules move randomly. 5. The time between collisions is much larger than the duration of collisions. 6. There are no intermolecular forces.

Question 60

Explain how Newton’s laws are used in the derivation of the equation: pV =1/3Nm(crms)^2 A derivation of the equation is not required.

Answer 60

Newton’s first law tells us that a gas molecule will move in a straight line until it collides with the walls of the container. Newton’s second law enables us to find the force on the molecule caused by its collision with the walls of the container. Newton’s second law tells us that: Force = change in momentum/ time Newton’s third law tells us that the force exerted on the wall is equal and in an opposite direction to the force exerted on the molecule.

Question 61

Given that: pV = 1/3 Nm(crms)^2 show that: p = 1/3ρ(crms)^2

Answer 61

The total mass of a gas made up of N molecules of mass m is Nm. The volume of the gas is V. The density is: Density =total mass / volume =Nm/V Given that: pV = 1/3Nm(crms)^2 Rearranging: p = 1/3 x Nm/V x (crms)^2 Therefore: p = 1/3ρ(crms)^2

Question 62

Calculate the temperature of a gas with an average kinetic energy of 5 × 10–22 J. E = 1.38 × 10−23JK^−1

Answer 62

mean kinetic energy = 3/2kT T = mean kinetic energy × 2 / 3k = (5 × 10^−22 × 2) / (3 × 1.38 × 10^−23) = 24.15 K

Question 63

Calculate the root mean square speed of 3 moles of oxygen gas O2 with an average kinetic energy of 3.05 × 10–22 J. The molar mass of oxygen gas O2 is 0.032 kg. NA = 6.02 × 1023mol−1

Answer 63

mean kinetic energy = 1/2m(crms)^2 To find the mass of one molecule of gas, m: m =Mass of gas/ Number of molecules in gas =Mrn/Nan =Mr/Na m = 0.032 / 6.02 × 10^23 = 5.32 × 10−26 kg Rearrange the first equation to get crms as the subject: crms = √mean kinetic energy × 2 / m | = √3.05 × 10^−22 × 2/5.32 × 10^−26 | = 107 m/s

Question 64

State the general characteristics of a Maxwell - Boltzmann distribution curve.

Answer 64

The area under the curve represents the total number of particles. This stays the same whatever the temperature. If the curve has been normalised the area under the curve is equal to one. As temperature decreases, the peak of the curve will shift further to the left.

Question 65

(Maxwell Boltzmann curve of 800k) sketch a curve for 200k

Answer 65

Peak shifted left (lower speed), taller, narrower,

Question 66

Why is the absolute scale used?

Answer 66

It doesn't arbitrarily depend on the properties of a given substance (eg. water's melting and boiling point for the Celsius scale). 0k (absolute zero) means that the particles have minimum internal energy.

Question 67

How does Brownian motion give evidence for the particle model of matter?

Answer 67

Smoke particles suspended in air can be seen to move randomly in all directions. This must be as a result of random collisions with particles making up the air.

Question 68

True or false: At a given temperature, all particles in a material have the same kinetic energy.

Answer 68

False. The kinetic energies will be randomly distributed around a central ‘most likely’ amount.

Question 69

How can you increase the thermal energy of a system?

Answer 69

We can increase it by heating it up or doing work on the object.

Question 70

Explain the energy changes that occur during a change of state.

Answer 70

During change of state the potential energy of the particles change but the kinetic energies don’t change.

Question 71

What equation can be used to determine the energy required to change the temperature of a substance?

Answer 71

Q = mcΔ𝜭 | Where Q = energy, m = mass, c = specific heat capacity, Δ𝜭 = temperature change.

Question 72

Give the equation to work of the energy for change | of state?

Answer 72

Q=ml Where Q = energy, m = mass, l = specific latent heat (‘of fusion’ if melting/freezing, ‘of vaporisation’ if condensing/evaporating)

Question 73

In an experiment to find ‘c’ for water, lots of energy input escapes to the surroundings. Will this lead to an over or underestimate of specific heat capacity?

Answer 73

● An overestimate. ● Specific heat capacity is calculated as: c = Q / mΔ𝜭 ● The energy input will be used, but the temperature change of the water will be lower than it should be due to the escaped energy - therefore c will be too high.

Question 74

What is an ideal gas?

Answer 74

A gas where: ● The gas molecules don’t interact with each other. ● The molecules are thought to be perfectly spheres.

Question 75

What is the ideal gas equation?

Answer 75

pV=nRT | Where p = pressure, V = volume, n = number of moles, R = the ideal gas constant, T = absolute temperature

Question 76

Assuming constant volume, how are the pressure and temperature of a gas related?

Answer 76

They’re directly proportional. | ie. P/T = constant

Question 77

Use the kinetic theory of gases to explain why a temperature increase leads to an increase in pressure.

Answer 77

● A temperature increase means the particles have more kinetic energy. ● More kinetic energy means a greater change in momentum during collisions with the container. There are also more frequent collisions. ● Change in momentum is proportional to force applied, and therefore to pressure as well.

Question 78

What equation links N, V, p, m and c?

Answer 78

pV = 1/3Nm(crms)^2

Question 79

What is meant by the root mean square speed?

Answer 79

The square root of the mean of the squares of the speeds of the molecules.

Question 80

What does the area under a Maxwell-Boltzmann curve represent?

Answer 80

The total number of particles.

Question 81

What are the units of the Boltzmann coefficient?

Answer 81

J/K

Question 82

The average kinetic energy of a particle in an ideal gas is equal to what?

Answer 82

1.5 kT

Question 83

True or false: ‘The internal energy of an ideal gas is proportional to absolute temperature’

Answer 83

True. In an ideal gas there is no ‘potential energy’ component in the internal energy. This means the internal energy is proportional to the kinetic energy (which is, in turn, dependent on temperature).