THERMODYNAMICS

Physics Y2

How can the energy of a system increase?

• Doing work on it.

• By heating it.

How can the energy of a system decrease?

• Losing heat to the surroundings.

• Changing state.

If the energy supplied causes the temperature of a body to increase...

Average speed and mean kinetic energy of particles increases.

Specific heat capacity

The amount of energy that is needed to raise the temperature of 1kg of a substance by 1°C / 1K without a change in state. Measured in J kg^-1°C^-1 or J kg^-1 K^-1.

ΔE =

mcΔθ

A low specific heat capacity means...

• A small amount of energy causes the temperature of the substance to change a lot.

• Little energy is required to heat or cool the substance.

• It stores and releases little thermal energy.

A high specific heat capacity means...

• A large amount of energy causes the temperature to only increase a little.

• A lot of energy is required to heat or cool the substance and

• It stores and releases a lot of thermal energy.

Specific heat capacity equation (2 substances)

m₁c₁(T₁ - Tᶠ) = m₂c₂(Tᶠ - T₂)

Assuming no heat is lost to the surroundings or container and there is no phase change (evaporation).

If a phase change occurs we must consider latent heat.

LHS is the hotter object initially.

Measuring the specific heat capacity of a solid:

1. A block with a known mass, m, is lagged with an insulator and an electrical heater is inserted into a drilled hole.

2. A thermometer is also inserted into the block to calculate the temperature rise (Δθ).

3. Water/oil can be added to the gap to increase thermal contact.

4. The heater is connected to a circuit with an ammeter in series to measure current I and a voltmeter in parallel to measure voltage V for an amount of time t.

5. mcΔθ = IVt

Measuring the specific heat capacity of a liquid:

1. A calorimeter with a known mass, m, is lagged with an insulator and an electrical heater is inserted into a drilled hole.

2. A thermometer is also inserted into the calorimeter to calculate the temperature rise (Δθ).

3. The heater is connected to a circuit with an ammeter in series to measure current I and a voltmeter in parallel to measure voltage V for an amount of time t.

4. Use a lid to reduce energy lost to the surroundings.

5. A stirrer is used to mix the liquid to keep thermal equilibrium and avoid hot spots.

6. E (total) = mcΔθ (liquid) + mcΔθ (calorimeter) to I t v = mcΔθ (liquid) + mcΔθ (calorimeter).

Work done by heating can cause a...

• Temperature increase, increasing the kinetic energy of the particles.

• Phase change, increasing the potential energy of the particles.

When a body experiences a change of state, work must be done against the...

• Attractive forces of the molecules.

• This enables the separation of the molecules.

• To expand, work must also be done against external pressure.

• The potential energy of the particles increases.

Heating curve

• When temperature increases, kinetic energy increases.

• When the graph is flat, temperature doesn't increase. The state is changing and the potential energy increases instead.

Specific latent heat

The amount of energy needed to change the state of 1kg of a substance without changing its temperature. Measured in J kg^-1.

Specific latent heat of fusion

The energy needed to change 1kg of a substance from solid to liquid without a change in temperature. Measured in J kg^-1.

Specific latent heat of vaporisation

The energy needed to change 1kg of a substance from liquid to gas without a change in temperature. Measured in J kg^-1.

E =

mL

Internal energy

The sum of the random distribution of kinetic and potential energies within a system of molecules.

Absolute zero

0K or -273°C. The point where average kinetic energy of molecules is 0J.

To convert from °C to K...

+ 273

To convert from K to °C...

- 273

Negative Kelvin is impossible because...

You can't have less than 0J of energy

Kinetic energy is directly proportional to...

Temperature in Kelvin as Kelvin starts at absolute zero, where KE = 0J

If T changes by a factor n in Kelvin, average speed changes by a factor of...

√n

Kinetic theory assumptions

• Gases contain a very large number of molecules.

• Molecules are in continuous random motion.

• The volume of molecules is negligible compared with the volume of the container.

• Collision time is negligible compared with the time between collisions.

• Collisions are elastic.

• Intermolecular forces are negligible, so potential energy is too.

• The molecules obey Newton's laws of motion.

For gases, you can't use average velocity because...

Molecules are constantly moving randomly in all directions, so it cancels to 0. Average speed is used instead

Kinetic theory equation

pV = 1/3 Nm<c²>

Kinetic theory equation derivation

When a molecule collides elastically with a wall, its change in momentum = -2mcₓ

Time between collisions =2L /cₓ

F = Δp/Δt = -2mcₓ / (2L/cₓ) = -mcₓ²/L

The force on the wall is equal and opposite, so = mcₓ²/L

p = F/A = mcₓ²/AL

pV = mcₓ²

For N molecules, take the average: pV = Nm<cₓ²>

Molecules move in the x, y and z directions: <c²> = <cₓ²> + <cᵧ²> + <c₂²>

<cₓ²> = 1/3 <c²>

Therefore: pV = 1/3 Nm<c²>

Why does the pressure increase when we heat a gas at constant volume?

• The average kinetic energy of the particles increases as kinetic energy is directly proportional to temperature, so the particles move faster.

• There are more frequent collisions between the particles and the walls of the containers as 2s = vt, so a greater speed causes more collisions per second.

• The collisions involve a greater change in momentum and therefore a higher force as F = m(v - u)/t.

• Pressure is force/ area therefore it increases too!

Pressure law

Pressure is directly proportional to temperature in Kelvin if volume and mass are fixed.

p₁/T₁ = p₂/T₂

Charles' law

Volume is directly proportional to temperature in Kelvin if pressure and mass are fixed.

V₁/T₁ = V₂/T₂

Boyles' law

Volume is inversely proportional to pressure if temperature and mass are fixed.

p₁V₁ = p₂V₂

The ideal gas equation

pV = NkT

N = no. of molecules

k = The Boltzmann constant

Ideal gas assumptions

• All molecules of a particular gas are identical

• The internal energy of the gas is entirely kinetic

• All molecules travel in straight lines

• Gravitational and electrostatic forces can be ignored

• All collisions between molecules and the walls of a container are completely elastic

• Newton's laws of motion apply

• The molecules move with random, continuous motion.

• Molecules take up negligible volume

Average kinetic energy of 1 molecule of an ideal gas =

1/2 m<c²> = 3/2 kT

1/2 m<c²> = 3/2 kT derivation

pV = 1/3 Nm<c²> and pV = NkT, so:

1/3 Nm<c²> = NkT

1/3 m<c²> = kT

m<c²> = 3kT

KE = 1/2 mv², so:

Average kinetic energy of 1 molecule of an ideal gas = 1/2 m<c²> = 3/2 kT

Black body

A perfect emitter and absorber of all wavelengths of radiation. Stars are modelled as black bodies

Intensity-wavelength graph for a black body

The continuous spectrum shows you it is a black body.

Shorter wavelengths cause a steeper gradient.

The peak is the wavelength with maximum intensity and depends on temperature.

The area under the curve is the total power emitted per unit area, so equals σT^4.

The luminosity is the area under the graph multiplied by the area of the star.

Luminosity

The total power output of an object measured in Watts.

Stefan-Boltzmann Law

L = σAT⁴

σ = The Stefan-Boltzmann constant

A = The surface area of the star (4πr²)

I =

L/4πd² or σAT⁴ / 4πd²

d = Distance to observer in m

Wien's Law

λ(max)T = 2.898 x 10^-3 mK

Wien's Law tells us...

Where the peak of a black body curve is.

As temperature increases, peak wavelength decreases.

This means frequency and wave energy increase.