Thermodynamics

Question 1

This graph shows how the temperature of a solid that is being steadily heated in a well-insulated container changes with time. Explain in terms of energy of molecules what is happening.
|......................................../  
|.....................\_\_\_\_\_\_\_/
|.................../
|................./
|\_\_\_\_\_\_/\_\_\_\_\_\_\_\_\_\_\_\_\_
|.../
|./

Answer 1

As temperature increases, particles move faster (vibrational or translational motion)
Kinetic energy increases on all of the sections with a positive gradient
The areas where the graph has a horizontal line indicate a change of state
Energy input at these points allow particles to break free of other molecules by breaking bonds, as separation between molecules increases so potential energy increases (rather than kinetic energy, so temperature does not change at these points)

Question 2

What is internal energy?

Answer 2

Internal energy is the sum of random distributions of the kinetic and potential energies of all particles in a system

Question 3

What is specific heat capacity?

Answer 3

The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1kg of the substance by 1°C
Q = mcΔθ or E = mcΔT

Question 4

What is unconventional about the potential energy of ice compared to water?

Answer 4

Ice is less dense than water so potential energy decreases during the change of ice to water

Question 5

What is specific latent heat of fusion?

Answer 5

The specific latent heat of fusion of a substance is the quantity of energy per unit mass required to change it at a constant temperature from a solid to a liquid
Q = Lm

Question 6

What is specific latent heat of vaporisation?

Answer 6

The specific latent heat of vaporisation of a substance is the quantity of energy per unit mass required to change it from a liquid to a gas
Q = Lm

Question 7

Why is specific latent heat of vaporisation higher?

Answer 7

Particles are further apart so it takes more energy to separate them

Question 8

Outline the method for calculating the specific heat capacity of a metal

Answer 8

Insulate a metal block with 2 holes in the top. Place a thermometer in one, and a heater in the other. Connect a voltmeter in parallel across the heater and an ammeter in series, then connect it to a ~12V power supply.
Measure the time, the voltage and current, the mass of the block and the initial and final temperature.
Energy supplied by heater = VIt
Energy gained by block = mcΔT
Therefore VIt = mcΔT, rearranging to find c
Or plot a temperature against time graph

Question 9

Describe the sources of error in the experiment to calculate the specific heat capacity of a metal

Answer 9

Energy is used to heat the lagging and the surroundings (assumed to be zero in calculations)
The top of the metal is not insulated
Long wires may be used, so resistance is high, meaning there is a voltage drop
There is an air gap between the block and the heater and the block and the thermometer (can be minimised by putting oil in the holes in the block)

Question 10

Explain the effects of the sources of error in the experiment to calculate specific heat capacity of a metal on the calculated value when compared to a textbook value

Answer 10

In the practical, energy is lost to the surroundings, so more energy is needed to raise the temperature of the substance, meaning calculated values of specific heat capacity are larger than a textbook value

Question 11

What are the assumptions of kinetic theory (or assumptions for an ideal gas)?

Answer 11

1. Molecules have negligible size
2. The molecules are identical
3. All collisions are perfectly elastic and the time of a collision is significantly smaller than the time between collisions
4. The molecules exert no forces on each other except during collisions
5. There are a very large number of molecules
6. The motion of the molecules is random

Question 12

Explain how the motion of gas particles in a container causes gas pressure

Answer 12

Gas particles have energy and collide with container walls
There is change of momentum of the particles
So there is a force (F = mv/t) on the particles
There is a force on the wall (Newton’s 3rd law)
Force acts over an area so there is a pressure (p = F/a)

Question 13

How can the distribution of molecular speeds explain the process of evaporation of a liquid? Explain what happens to the temperature of the remaining liquid

Answer 13

In evaporation, a small number of particles have sufficient energy to break away and become a gas.
The average temperature of the liquid drops, but it is re-established as it absorbs energy from the surroundings

Question 14

Explain what is meant by the root-mean-square speed and why this value is used

Answer 14

The root-mean-square speed is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative.
Velocity is not useful on its own because the value will not be representative, and by doing rms, it is a close of the true average speed.
It is usually given the symbol

Question 15

What is Boyle’s Law?

Answer 15

The volume of a fixed mass of gas is inversely proportional to its pressure provided the temperature remains constant
P = k/V , P1V1 = P2V2

Question 16

What is Charles’ Law?

Answer 16

The volume of a fixed mass of gas is directly proportional to absolute temperature
V1/T1 = V2/T2

Question 17

What is Pressure Law?

Answer 17

The pressure of a fixed mass of gas is directly proportional to its absolute temperature provided its volume remains constant
P1/T1 = P2/T2

Question 18

What is the mathematical relationship that is useful for comparing 2 situations concerned with pressure, temperature and volume?

Answer 18

P1V1/T1 = P2V2/T2

Question 19

What is a mole?

Answer 19

One mole of any substance is the amount of that substance which contains the same number of particles as 12g of C-12 (6.02x10^23)

Question 20

What is an ideal gas?

Answer 20

An ideal gas is one that follows pV=nRT and the ideal gas equation, and follows the gas laws. It must be at high temperature and low pressure when intermolecular forces are negligible.
For gases at high pressure and low temperature, attractive forces may not be negligible so the gas will behave in a “real” way

Question 21

Derive (1/2)m = (3/2)kT

Answer 21

pV = NkT
pV = (1/3)Nm 
NkT = (1/3)Nm
kT = (1/3)m 
3kT = m 
(3/2)kT = (1/2)m

Question 22

What are the main steps to derive pV = (1/3)Nm ?

Answer 22

First, use F = m(v-u) / t to find an expression for F
Then s = vt and rearrange for t
Then, P = F/a using original expression for F
There is a large number of particles, so replace with
Add 1/3 because the movement happens in 3 directions (3pV then rearrange to find 1/3)