# Matter: Very simple

OCR B- Advancing Physics - Chapter 13

- Created by: Morgan
- Created on: 04-04-10 14:06

## Measuring Temperature

The Celsius scale, based on the ice-point and the steam point, is a useful scale for everyday life. However, there are a few drawbacks:

- Thermometers which use different thermometric properties only agree at the points calibration.
- The Celsius scale is
**not**an absolute scale, so 20ºC is**not**twice as hot as 10ºC.

Therefore an **absolute scale** is used. There is a lowest possible temperature called absolute zero. Absolute zero is given a value of zero Kelvin, 0K, on an absolute temperature scale.

At 0K all particles have minimum possible kinetic energy – everything pretty much stops. At higher temperatures, particles have more energy. In fact with the Kelvin scale, a particle’s energy is proportional to its temperature

K = C + 273

## Three Gas Laws:

**Boyle’s Law:**At a constant temperature the pressure P and the volume V of a gas are inversely proportional.

PV = Constant

**Charles’s Law:**At a constant pressure, the volume of a gas is directly proportional to its absolute temperature T.

V/T = Constant

**The Pressure Law:**at a constant volume, the pressure P is directly proportional to the absolute temperature T.

P/T = Constant

## Ideal Gas Equation:

By combining all these laws you get the idea gas equation:

PV/ T = Constant

· The constant in the equation depends on the amount of gas used. The amount of gas can be measured in moles.

· The constant then becomes nR, where R is called the molar gas constant, which is 8.3Jmol-1K-1.

This gives the final equation for the ideal gas as:

PV = nRT

## Particle In a Box:

1. **Particles velocity is proportional to pressure.** The faster the particle the greater the momentum, so the larger the force on the wall. Particle takes less time to travel across the box, so hits wall more **often.** And as pressure = force / area, the pressure will be greater.

2. **The number of particles N, is proportional to pressure.** Instead of one particle hitting the wall, lots are. Each particle exerts a pressure on the wall so the total force on the wall is proportional to the number of particles. So pressure is proportional to force/area, so pressure is proportional too.

3. **The volume of the box is inversely proportional to the pressure.** If you have a smaller box, particle have less distance to travel before hitting a wall, so more frequent collisions so increased force. Because area is now smaller, this makes the pressure greater.

4. **Particles travel in random directions at different velocities.** To take account for the different velocities you take the average of the square of the velocities called the mean squared speed V².

**Pv = 1/3 Nm V²**

## Assumptions:

In the kinetic theory, physicists picture gas particle moving at high speeds in **random directions**. To get the previous equations some simple **assumptions** are made.

1. The gas contains a **large** number of particles.

2. The particles move **rapidly** and **randomly.**

3. The motion of the particles follows **Newton****’s laws**.

4. Collisions between the wall or other particles are **perfectly elastic**.

5. There are **no attractive forces** between the particles.

6. Any forces that act during collision are **instantaneous.**

7. Particles have a **negligible volume** compared with the volume of the container.

## Random Walk

1. There is **NO** way you can record the random motion of all the particles in a gas. Instead you can use a **model.**

2. A random walk assumes that each particle **starts in one place**, **moves N steps** in a **random direction**, and ends up some where else.

3. What is really useful is that the **average distance** moved in those N steps is **proportional to** **ÖN.**

4. The distance the particle moves before a collision is normally 10-7m. So it is no wonder **diffusion** is quite a **slow process**, even if the particles are travelling at high speeds.

## Special Heat Capacity:

**Special heat capacity** of a substance is the amount of energy needed to raise the temperature of 1 Kg of the substance by 1k.

Changing the temperature of an object involves changing its internal energy, the total potential and kinetic energy or the particles. The energy transfer required to change the temperature of an object depends on:

· The temperature change.

· The mass of the object

· The material the object is made of.

Energy change = mass x specific thermal capacity x change in temperature

**ΔQ = mcΔT**

The particles of gas collide with each other all the time. Some of these collisions will be 'head-on' while other will be 'shut from behind'. As a result of the collision, energy will be transferred between particles. Some particles will gain speed in a collision others will slow down. The energy of a particle changes.

## Internal Energy:

Internal energy is the sum of kinetic energy and **potential energy**. All things (solid, liquid or gases) have energy contained within them. The amount of energy contained in a system is called the internal energy – it’s found by summing the kinetic and the potential energy of all particles.

**Internal energy is the sum of the kinetic and potential energy of the particles within a system.**

But **HOW** do you do this when the particles all have different speeds, so different kinetic energies? Answer by finding the **average kinetic energy**.

There are 2 equations to find the pV of a gas, If you equate the two you get another useful equation. ½mv² is the average kinetic energy of an individual particle. The internal energy of an ideal gas is the product of the average kinetic energy of its particles and the number of particles in it, So the average kinetic energy is **directly proportional to absolute temperature**.

## Average Kinetic Energy is Proportional to Absolute

½**mc****²=3nRT/2N**

So the internal temperature must also be dependent on temperature:

**A rise in temperature will cause an increase in the kinetic energy of a particle, meaning a rise in internal temperature.**

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