G484: Module 3 - Thermal Physics

All topics inside module 3 of G484: The Newtonian World  OCR A2 Physics

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Solids, Liquids and Gases

Phase: whether a substance is a solid, liquid or a gas. 

Solids: Contain many molecules packed closely together. Particles vibrate about fixed positions in a regular lattice. They're held in position by strong forces of attraction.

Liquids: Also contains many molecules pack closely together, however the patten in a liquid is not as regular as in a solid, and varies from moment to moment. Particles do not have much space to move around in, but they can glide over one another.  

Gases: Vastly increased spacing in a gas. There is no arrangement of the particles at all. Particles are free to move around with constant random motion. There are no forces of attraction between particles in an ideal gas

Density: Mass per unit volume. 

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Brownian Motion

As a solid is heated, its temperature rises and the kinetic energy of its molecules therefore increases. The increase in KE results in greater vibration around its equilibrium. 

In a liquid the same effect takes place. But this time, a small amount of translational kinetic energy will be added to the increase in vibrational KE, since the molecules are now able to move from place to place.

The motion of molecules in a gas is invisible to the naked eye. However, if smoke is introduced into a glass container and is illuminated and viewed through a microscope, the effect of molecular motion can be seen. The motion is known as Brownian Motion, and was first observed by Thomas Brown when he was examining pollen grains in water. He saw that they were never completely still but always "shuddered" around. It was the first direct evidence that molecules are in perpetual motion. 

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The Kinetic Theory and Gas Pressure

Pressure: Force per unit area. The force required is the force perpendicular to the area. 1Pa = 1N/m^2

Kinetic model of a gas: Macroscopic - description of a gas on a large scale. It has mass and a volume equal to the volume of the container it is in. The gas exerts a pressure on the walls of the container. Microscopic - collection of a large number of moving molecules that hit one another and the walls of their container. 

Assumptions: Gas consists of a large number of molecules in rapid, random motion. Collisions between molecules and between the molecules and the walls of the container are elastic. The gravitational force on the molecules is negligible. No intermolecular force exists except during collisions. The total volume of the molecules is negligible compared with the volume of the container. 

Pressure exerted by a gas depends on: 1. Volume of the container - increasing the volume decreases the frequency of collisions as molecules have further to travel in between collisions. Increase in volume, decrease in pressure. 2. Number of molecules - increasing the no. of molecules increases the frequency of collisions between the molecules and the container, so increases the total force exerted by all the collisions. 3. Mass of molecules - according to Newton's 2nd law, force is proportional to mass, so heavier molecules will exert a greater force, and therefore more pressure. 4. Speed of molecules - the faster the molecules are going when they collide, the greater the change in momentum and force exerted, so therefore more pressure. 

pV (proportional to) Nmc^2   (c^2 is the means square speed - represents speed of typical molecule)

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Internal Energy

Internal Energy: the sum of the random distributions of kinetic and potential energies of all the molecules in the body.

Ideal gas: a gas that has internal energy only in the form of random KE. 

Factors affecting internal energy:

1. Temperature - if the temp of a system rises, the molecules travel more rapidly, their KE rises so therefore their internal energy rises.

2. Pressure - If pressure falls with no change in temp, then internal energy is unchanged in an ideal gas. If gas is not ideal, then molecules will attract each other (gas expanding), there must have been some work done on the molecules to pull them apart. This means that there is a higher PE and a higher internal energy, even though temp hasn't changed.

3. State - a change in state doesn't involve a change in temp. Therefore KE component of internal energy doesn't change, but PE does. Changing a solid into a liquid at the same temp involves an increase in volume and therefore a rise in internal energy. There is a rise in internal energy as ice melts (breaking down crystal structure requires energy).

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Thermal equilibrium: two objects at the same temperature, e.g. food in an oven cannot get hotter than the oven temp itself. Once it is the same temp as the oven, the food will be in thermal equilibrium with the oven. It occures then there is zero resultant energy transfer between them.

Temperature determines the direction in which thermal energy will be transferred. Thermal energy is transferred from a region at a higher temp to a region of lower temp. The earth is hotter than the space that surrounds it, so the energy flow from earth to space is much greater than the flow from space to earth. 

The absolute scale of temp exists. It doesn't depend on any property of a substance. It starts from zero, the temp where a substance has minimum internal energy. 

Absolute zero is zero kelvin, 0K. The triple point of water (where it exists in the solid, liquid and gas states simultaneously) is 273.16K exactly. 

T(K) = t('C) + 273.15

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Specific Heat Capacity

Specific heat capacity: the quantity of thermal energy required to raise the temperature of a unit mass of a substance by a unit temperature rise. (energy needed to raise the temperature of 1kg by 1*C or 1K). E=mc(delta theta)

Method for S.H.C.

1. Heat the substance with the heater. 2. With an ammeter and voltmeter attatched to you electric heater you can work out the energy supplied. Calculate the energy (E) using   E = VIt, where V is the heater voltage, I is the current and t is the time in seconds. 3. Put data into   E = mc(delta theta) to calculate c.

The value you end up with for c will probably be too high by quite a long way, This is because some of the energy from the heater gets transferred to the air and the container. 

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Latent Heat

When you head a substance you increase the KE of the molecules within it, therefore increasing its internal energy. However when a substance changes state, internal energy changes but temp doesn't. This is because the change of state alters the PE of the molecules, not their KE. Energy is required to change a solid to a liquid or a liquid to a gas. Because this increases the internal energy of the substance, the molecules must gain PE when the substance melts or boils. 

Specific latent heat of fusion of a substance is the quantity of energy per unit mass required to change is at constant temperature from a solid into a liquid.

If ice falls into the sea from a glacier, it will become an iceberg in the water and will require a very large amount of thermal energy before it all changes into water. 

Specific latent heat of vaporisation of a substance is the quantity of energy per unit mass required to change it at constant temperature from a liquid into a vapour.    E = ml

*a vapour can be changed back into a liquid by applying pressure to it. A gas cannot be liquefied by pressure alone. 

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Boyle's Law

Boyle's law states that the volume V of a fixed mass of gas is inversely proportional to the pressure p exerted on it, provided the temperature is kept constant. 

Experiment to demonstrate this law: uses a long tube, closed at one end and containing air above some oil. The pressure on the oil can be increased by means of a pump, and the pressure exerted on the air by the oil is indicated by a pressure gauge. The volume of air in the tube can be measured from a scale behind the tube.

The apparatus can be pumped up to a high pressure and then very slowly vented. As the pressure gauge reads the values given, the volume is slowly recorded. It is important to do the experiment slowly in order to keep the temperature constant. A gas cools as it expands, and time must be allowed for the temp to be constant. 

The unit given for pV is Nm. To get the value in Nm, the volume needs to be in m^3 and the pressure in Pa. 

It is difficult to check the shape of a graph showing an inverse proportion of p and v. If a graph is to be plotted, then a straight line can be plotted from p against 1/V.

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The Ideal Gas Equation

Boyle's law doesn't stand if the gas is close to its boiling point, or if very high pressures are used. Under these conditions the molecules themselves are occupying a considerable fraction of the volume of their container. The kinetic theory of gases is therefore not as accurate under these circumstances. 

If a gas behaved ideally, Boyle's law would apply exactly. An ideal gas is imaginary but at low pressures, gases such as hydrogen, helium and air behave in a similar way to an ideal gas. This is because at atmospheric pressure the volume of the gas molecules themselves is around a thousandth of the volume of their container. By working at much lower pressures, the fraction becomes even smaller. 

For a fixed mass of an ideal gas at constant pressure, its volume V is proportional to the ideal gas temperature T (K). 

Combine this law with Boyle's law: V/T = constant, and pV = constant, therefore, pV/T = constant. 

From the definition of the ideal gas scale, this equation is exactly true for an ideal gas. 

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The Amount of Substance

Avogadro's law: equal volumes of gases under conditions of equal temperature and pressure contain the same number of molecules. 

Avogadro's constant: NA is 6.02x10^23

One mole of any substance contains 6.02x10^23 particles.

n=N/NA n=M/Mm

n: no. of moles, N: number of particles, M: mass of substance, Mm: molar mass

if pV/t= constant, the constant in the equation depends on the amount of gas used. The amount of gas can be measured in moles, n. The constant then becomes nR, where R is the molar gas constant (8.31J/mol K).

Putting that into the equation gives:

pV/T=nR  or pV=nRT

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The Boltzmann Constant

The Boltzmann Constant: the gas constant for a single molecule, 1.3807x10^-23(J/K)

It is useful when considering the gas equation for molecules rather than moles. R is the gas constant for one mole of molecules. The Boltzmann constant, k, is the gas constant for one single molecule. pV=nRT => nR is the constant for n moles of gas. Therefore, in terms of k, the same value must be Nk, where N is the total number of molecules. 

Therefore, pV=nRT or pV=NkT  

This is called the equation of state of an ideal gas.

The mean kinetic energy E of a single molecule can be obtained in terms of the Boltzmann constant:  E=3/2 x kT

This gives the mean random translational KE of an ideal gas, that is its internal energy. It also shows this energy is directly proportional to the temperature in K. 

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