Topic 5: Thermal physics

Brownian motion

random movement of particles; they change velocity and direction randomly

What causes Brownian motion?

Collisions between smoke molecules and the much smaller invisible air molecules

Use kinetic theory to explain why a gas in a container exerts a pressure on that container.

When a gas molecule collides with a wall, there is a change in direction…change in momentum

The wall exerts a force on all the particles, which is equal to the rate of change of momentum of the particles. (Newton's second law:$F=\frac{\Delta mv}{t}$ )

The particles exert an equal and opposite force on the wall

The gas therefore exerts a pressure on the wall

Using kinetic theory, explain Boyle's law.

Container's volume decreases

Particles hit the wall more frequently

Change in momentum remains the same — the mean speed in unchanged at a constant temperature

Total force increases as the frequency does, so the pressure increases

Using kinetic theory, explain the pressure law.

Temperature increases, so does mean kinetic energy.

Change in momentum increases…force increases

To keep volume constant, pressure must increase as $P=\frac{F}{A}$

Using kinetic theory, explain Charles’ law

Temperature increases at constant pressure

Each collision has a greater change in momentum…greater force

For pressure to remain constant, the volume of the container must increase since $P=\frac{F}{A}$

What do N and n stand for in thermal physics?

n = number of moles

N = number of molecules

Boyle's law

$P\alpha\frac{1}{V}$ at a constant temperature

Isothermal change

changes that occur at a constant temperature

Charles’ law

$V\alpha T$ for a fixed mass of gas at constant pressure

Isobaric change

a change at a constant pressure

Pressure law

$P\alpha T$ at a constant volume

Ideal gas law

$PV=nRT$ where n = moles and R = the ideal gas constant (8.31)

$PV=NkT$ where N = no. of gas molecules and k = Boltzmann’s constant (1.38×10^-23)

Internal energy

sum of the kinetic and potential energies of all the particles

How can the internal energy of a system be increased?

- heat the system

- do work on the system

What is 0K in celsius?

-273°C

Specific heat capacity (c)

the energy required to raise the temperature of 1kg of a substance by 1K without a change in state

Specific latent heat (l)

the energy required to change the state of 1kg of a substance without a change in temperature.

Describe the conditions in which an experiment should be run so that gas tested will behave most like an ideal gas.

low pressure

temperature far above boiling point

mass, moles and molecules formula

$N=\frac{m}{M}\cdot Na$ where N = no. of particles, m = mass, M = atomic mass and Na = Avogadro’s constant (6.02×10^23)

First law of thermodynamics

$\Delta U=Q-W$ where U is the change in internal energy, Q is heat added to the system, and W is work done by the system.

Ideal gas

gas molecules don’t interact with each other

molecules are thought to be perfect spheres

Kinetic theory of ideal gas assumptions (6)

no intermolecular forces act on the particles

particles move randomly

particles follow Newton’s laws

volume of the particles is negligible compared to the volume of the container

all collisions are elastic

the time for a collision is negligible compared to time between collisions

root mean squared speed

square root of the mean of the squares of the speeds of the particles or

$$\sqrt{\frac{\left(c^2+c^2+c^2\ldots\right)}{N}}$$

area under a pressure volume graph

work done

derivation of $pV=\frac13Nmc^{2}$ (kinetic theory model)

$$p=\Delta mv$$

$$F=\frac{\Delta mv}{t}=\frac{p}{t}$$

$$P=\frac{F}{A}$$

$$c² = v² + v² + v²$$