Topic 3: Thermal Physics

3.1 Thermal concepts

This chapter is an introduction to thermal physics. It introduces the concepts of temperature, heat,

internal energy and thermal equilibrium.

You should:

• understand the concept of thermal equilibrium;• relate the Kelvin and Celsius scales of temperature;• know that internal energy is the total kinetic energy of the molecules of a system plus the potential energy associated with the molecular forces.

TemperatureIntuitively: concept of “hotness” or “coldness” of a substance with respect to something else.

To measure the temperature of a body we need to find a property of the body that changes as the “hotness” changes.

In 1742, Andreas Celsius created the temperature scale that is known by his name.

0°C – Freezing point of water100°C – Boiling point of water

Thermal Equilibrium

Two or more bodies are in thermal equilibrium when they have the same temperature.

Body A and body B are each in thermal equilibrium with body C. Therefore they are in thermal equilibrium with each other and hence have the same temperature (Zeroth Law of Thermodynamics).

Absolute temperature scale

0 K = -273.15 °C or 0°C = 273.15 K

T = TC + 273.15

TC = T -273.15

For practical purposes:

T = TC + 273

TC = T -273

The temperature scale used in Physics is the absolute temperature scale or Kelvin scale. Its unit is the kelvin (K)

Temperature has a lower limit

0 K or absolute zero

Heat As Energy

Heat is energy that is transferred from one body and into another as a result of a difference of temperature.

Thus, when a hot object is brought in contact with a colder body, heat will be transferred to the colder body and increase its temperature. We say that the colder body has been “heated”.

Heat and work, unlike temperature, pressure, and volume, are not intrinsic properties of a system.

Internal EnergyAll substances consist of molecules in constant motion. They therefore have kinetic energy.

In addition, there are forces between molecules (electrical in nature). Increasing the average separation of two molecules requieres work to be done. This work goes into potential energy associated with intermolecular forces.

Internal energy is the total kinetic energy of the molecules of a sustance, plus any potential energy associated with forces between the molecules.

The heat that is transferred from a hot to a cold body increases the internal energy of the cold body (and decreases the internal energy of the hot body by the same amount

Temperature, again

The absolute temperature is a measure of the average kinetic energy of the molecules of a substance. The average kinetic energy of the molecules is directly proportional to the absolute temperature in kelvin.

We therefore have a relationship between a microscopic concept and a macroscopic concept.

A hot body is brought into contact with a colder body until their temperatures are the same. Assume that no other bodies are around. Is the heat lost by one body equal to the heat gained by the other? Is the temperature drop of one body equal to the temperature increase by the other?

A body at a given uniform temperature of 300 K and internal energy 8 x 106 J is split into two equal halves.a) Has any heat been exchanged?b) What is the temperature of each half?c) What is the internal energy of each half?

The giant hornet Vespa mandarinia japonica preys on Japanese bees. However, if one of the hornets attempts to invade a bee hive, several hundred of the bees quickly form a compact ball around the hornet to stop it. After 20 minutes the hornet is dead, although the bees do not sting, bite, crush, or suffocate it.

Why, then, does the hornet die?

Confusion around the concept of “thermal energy”

Heat transfer (conduction)Thermal conduction is the process by which a temperature difference causes the transfer o thermal energy from the hotter region of the body to the colder region by particle collision without there being any net movement of the substance itself.

Conduction can occur in solids, liquids and gases.

Gases: Due to the collision between fast and slow moving particles where kinetic energy is tranfered from the fast to the slow particle.Liquids: Due to increased vibrational energy. Because the majority of the particles are coupled to other particles they also begin to vibrate more energetically.

Solids: Two ways. Similarly to liquids or by mobile electrons.

Heat transfer (convection)

Thermal convection is the process in which a temperature difference causes the mass movement of fluid particles from areas of high thermal energy to areas of low thermal energy (the colder region).

Liquids and gases can transfer heat readily by convection.

Heat tranfer (radiation)

Thermal radiation is energy produced by a source because of its temperature that travels as electromagnetic waves. It does not need the presence of matter for its tranfer.

Thermal radiation is mainly electromagnetic waves in the infra-red region of the electromagnetic spectrum at temperatures below 1000°C.

The mole, molar mass and Avogadro’s number

The mass of an atom is exceedingly small. For example, the isotope carbon-12 is 1.99 x10-23g.

In 1961 the International Union of Pure and Applied Chemistry defined the masses of atoms relative to carbon-12 that was assigned a value of 12.0. Therefore, the relative atomic mass is defined as the mass of an atom when compared with 1/12 the mass of carbon-12 atom.

Mass of carbon-12 = 12.000 uMass of oxygen = 16.000 u = 16/12 Mass of carbon-12

MoleThe SI fundamental unit for the amount of a substance is the mole (mol).

The mole is the amount of substance that contains as many particles (atoms, molecules) as there are in 12 g of carbon-12

Avogadro found that equal volumes of gases at the same temperature and pressure contained the same number of particles. One mole of any gas contains the Avogadro number of particles NA=6.02 x 1023, and it occupies 22.4 dm3 at 0°C and 101.3kPa pressure (STP).

Molar mass of carbon-12 = 12 g/molMolar mass of oxygen = 16 g/ mol

Molar mass

M = m/nWhere M is the molar mass (g/mol) , m is the mass (g), and n is the amount of substance in moles.

n = N/NAWhere N is the total number of particles

Important note: When using the mole, the atoms or molecules should be clearly stipulated. For example, one mole of copper atoms contains 6.02 x 1023 cooper atoms. One mole of nitrogen molecules (N2) contains 6.02 x 1023 of nitrogen molecules and 12.04 x 1023 nitrogen atoms.

Example

1. Calculate the number of moles of oxygen molecules contained in 64 g of oxygen gas, O2.

2. Calculate the number of oxygen molecules in part 1 of this example.

3. Determine the volume of oxygen gas that would be present at STP.

4. Calculate the mass in 0.75 mol of carbon dioxide gas.