Thermal Physics

Thermal Concepts

Thermal Concepts

TemperatureThe absolute temperature scale (measured in Kelvin and with a minimum value of zero Kelvin) is used in physics calculations.

(Where a change of one Kelvin equals a change of one degree Celsius)

(i.e. The KE of the particles is directly proportional to the temperature)

Kelvin Temperature = Celsius Temperature + 273

The absolute (Kelvin) temperature of a body is a measure of the average amount of kinetic energy that each of its molecules have.

Thermal Equilibrium

When two bodies are at the same temperature as each other, they are in thermal equilibrium.

This leads to the ‘Zeroth law of thermodynamics’: If two bodies A and B are separately in thermal equilibrium with body C, they are also in thermal equilibrium with each other and thus have the same temperature.

Link – Thermal equilibrium Link – Heating a solid

Heat and Internal Energy

We know that work can be done on a body, causing energy to be transferred to it mechanically (by a force moving through a distance).

The only other way that energy can be transferred is by heat transfer:

Note: It is common to mistakenly say that a body ‘contains heat energy’. This is wrong. In this sense we need to refer to internal energy:

‘Heat’ is the energy that will flow between two bodies that are not in thermal equilibrium and that thus have different temperatures.

Note: While the potential energy of the particles results from their position and the forces between them, the kinetic energy of the particles is not only from their vibration.

They may also have KE because they are spinning, moving from place to place etc. The many different ways in which a particle has energy are sometimes known as ‘degrees of freedom’.

In any body, the internal energy of the body is equal to the sum of the kinetic energy and potential energy of all the particles.

molecules

Temperature and Internal Energy - Link

Moles and The Avogadro Number

The number of molecules in a substance is measured in ‘moles’. Just like ‘a dozen’ means twelve of something, ‘one mole’ means 6.02 x 1023 molecules of something.

One mole of a substance contains the same number of molecules as in 12 grams of Carbon-12.

The Avogadro number (NA) is equal to the number of

molecules in 12 grams of Carbon-12 (NA= 6.02 x 1023)

The molar mass (M) is the mass in grams of one mole of a particular substance.

Note: the mass number of an element is equal to the molar mass for atoms of an element.E.g. One mole of Nitrogen atoms will have mass 14g.

E.g.1 The mass number of Helium is 4. How many atoms are in 4kg of Helium?

A. Mass no. is 4 so molar mass is 4g.4000 g / 4g = 1000 moles1000 x NA = (1 x 103) x (6.02 x 1023)

= 6.02 x 1026 atoms

E.g.2 The molar mass of iron atoms is 56 g mol-1 and its density is 7.9 g cm-3.

a. Find the mass of one atom of Iron.b. Calculate the number of iron atoms in one cubic

metre of iron.

E.g. 2 The molar mass of iron atoms is 56 g mol-1 and its density is 7.9 g cm-3.

a. Find the mass of one atom of Iron.

b. Calculate the number of iron atoms in one cubic metre of iron.

a. If one mole of atoms has mass 56g then one atom will have mass = 56 ∕ NA

= 56 ∕ (6.02 x 1023)

= 9.3 x 10-23g

b. One cm3 has mass = 7.9 g

So one m3 has mass = 7.9 x (100x100x100) g = 7.9 x 106 g

So no. of iron atoms per m3 = 7.9 x 106 / 9.3 x 10-23

= 8.5 x 1028 atoms

Further calculations with moles

The number of moles of a substance (n) can be determined form the total mass (m) divided by the molar mass (mass per mole, M), usually both measured in grams:

Similarly if you knew the total number of molecules (N), you could find the number of moles (n) from…

n = m M

n = N NA

E.g.

a. Calculate the number of moles of oxygen atoms in 40g of oxygen.

N = m / M = 40 / 16 = 2.5 moles

b. Calculate the number of moles of oxygen molecules (O2) in 40g of oxygen.

N = m / M = 40 / 32 = 1.25 moles

c. A sample of fluorine gas contains 20 x 1023

atoms of fluorine. Calculate the number of moles present.

N = N / NA = 20 x 1023 / 6.02 x 1023 = 3.3 moles

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