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Revision:Thermal Physics and Properties of Matter

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3.1 The atomic model of matter and states of matter

3.1.1

There are 4 states of matter, Solid, Liquid, Gas, Plasma

Solid ... rigid shape and constant volume ... the forces between molecules far outweigh the thermal energy held by the molecules, and so the molecules form a rigid lattice (in which they vibrate).

Liquid ... constant volume (over as short term, but eventually evaporation occurs) but takes on the shape of it's container ... The thermal energy possessed by the molecules is more significant, but still not enough to allow them to completely overcome the forces between them. As a result, the molecules are free to move within the liquid, but only exceptionally fast molecules can escape it.

Gas ... Fills any container it is placed in (no constant volume or shape) ... The thermal energy between the molecules far outweighs the intermolecular forces, and so they move randomly, with minimal interactions between molecules.

Plasma ... If a gas is heated enough, then the molecules lose their electrons, and the ions and atoms form something similar to a gas, with random particle movement.

Most of the matter in the universe is plasma (that's what you make stars from) but most of the matter on earth is solid/liquid/gas...

3.1.2

As temperature increases, thermal energy increases. Thus, as a solid gets hotter, the vibrations of the molecules become larger and large, to the point where they break out of their rigid lattice and are free to move around randomly. As liquids are heated, more and more molecules have sufficient energy to completely overcome the intermolecular forces between them, and break away. eventually all the molecules are moving randomly with no significant forces between them. As a gas is heated, the electrons of the molecule/atoms are excited by the increased energy, to the point where eventually the electrons are excited enough to completely escape the molecule and move independently, thus creating a plasma ... In each case the reverse is true, as thermal energy decreases, the forces between particles pull them back form gas -> liquid -> solid.

3.2 Thermal concepts

3.2.1

Temperature is considered to be the hotness or coldness of an object as measured by a thermometer ... If two objects are of the same temperature, then there will be no net energy transfer between the two ... On a microscopic level, temperature is the average kinetic energy per molecule of the molecules in the substance.

Heat is the energy transferred between objects when they change temperature, and moves from areas of high temperature to areas of low temperature ... ie the lower temperature object is heated :)

Internal energy is the total energy related to the thermal motion of the molecules in a substance. This includes both vibrational and translational motion, and comprised of both the kinetic and potentials energies of the molecules.

3.3 Specific heat capacity, specific latent heat and 'heat transmission'

3.3.1

Specific heat capacity is a property of a substance in general, while heat capacity is the property of a particular body, otherwise they are identical. Their purpose is to relate internal energy change to temperature change, as different amounts of energy will be required to cause a given change in temperature in the same mass of different substances

$\Delta Q = m \times C \times \Delta T$ ( ie change in internal energy = mass x heat capacity x change in temp ).

3.3.2

A given mass of different substance may contain different numbers of molecules, of different masses and types. If the same amount of energy is added to two different substances, it will be distributed among the molecules, but the average E_k of these molecules will be different. Thus, the change in temperature will be different, and so different heat capacities are necessary.

3.3.3

Determining heat capacities - There are basically two ways to do this, either by adding a certain amount of energy to a substance and measuring the temperature change, or by mixing two substances at different temperatures, one of which has a known heat capacity, which will allow the other to be calculated.

Direct - Energy is applied to the substance using an electrical current. For a liquid, this is in the form of a heating element being placed in the liquid, and for a solid, holes are cut in the block for an electric heater and thermometer. The total amount of energy supplied by such an electric heater is VIt , where V = the potential difference across the heater, I = the current running through it and t = the time the heater is on for (in seconds).

Therefore, $VIt = m \times C \times \Delta T$ and the only unknown is C.

Mixtures - Water has a heat capacity of 4800 (J/kg deg-c). If 250 g of water (250 ml) at 25c has placed into it a metal block of unknown heat capacity at 30c, then the temperature of the resulting mixture can be measured once it reaches equilibrium. Thus, the amount of heat gained by the water can be calculated, but $\Delta Q = 0.250 \times 4800 c \Delta T$ . Since heat gained = heat lost, the $\Delta Q$ can then be subbed into the equation for the block ( Nb, it, and $\Delta T$ must both be negated. Though these cancel out and can be ignored ). Thus, the C value for the block can be found.

3.3.4

Describe transformations between states in macroscopic and microscopic terms ... sounds like 3.1.2 to me...

Melting/Freezing -Transfer between solid and liquid.

Solids -> rigid shape and constant volume. Liquid -> constant volume, shape determined by container. Solid -> liquid - Molecules vibrate faster and faster eventually reaching the point where they break away from their lattice structure and are able to move freely through the substance, thus becoming a liquid. Liquid -> solid - molecules are slowed by the removal of energy, eventually the intermolecular forces are dominant enough to pull them into a lattice, creating a solid.

Vaporisation/Condensation - Transfer between liquid and gas.

Liquids -> constant volume, shape determined by container. Gas -> No constant volume, shape fills container. Liquid -> Gas ... molecules require a certain E_k to completely escape from the surface of the liquid, as temp increases, faster molecules can escape, and eventually all do, forming a gas. Gas -> Liquid - As energy is removed, molecules slow down, eventually the intermolecular forces become dominant enough to hold the molecules together in a liquid.

Sublimation - (direct) Transfer between from a Solid to a gas.

Solids -> rigid shape and constant volume. Gas -> No constant volume, shape fills container. Solid -> Gas - At low pressures, when the molecules in a solid gain enough energy to escape the lattice, they already have sufficient energy to completely escape the other molecules (because the low pressure dictates very few molecule - molecule interaction). As a result, the solid changes directly to a gas. (This is why dry ice doesn't turn into a liquid)

3.3.5

When substances change state, there is a period where energy is added, but no change in temperature occurs (ie latent heat of fusion/vaporisation ). This is because, during this period, the energy goes towards increasing the potential energies of the molecules as they move away from each other, and so the kinetic energy does not change, and so the temperature remains constant.

3.3.6

Solving problems with specific heat capacity and specific latent heat. This is normally done by breaking the calculation up into a series of steps...if heat is being added, the solid (ice for example) is heated up to 0c, then energy is required for the latent heat of fusion, then the resulting water is heated...the heat of vaporisation, then water vapor is heated. In each case, different states of water (or anything else) will have different specific heat capacities, so this must be accounted for.

3.3.7 : Conduction, convection and radiation

Conduction - Heat is transferred through solids, when heat is applied to one end of a metal bar, this heat will slowly travel through it to reach the other end. On a molecular level, when the atoms at one end are heated, they vibrate more. These vibrations cause the molecules next to them to vibrate more, and so the increased vibrations, and so the heat and temperature are propagated through the material.

Convection - This is where heat is transferred through a liquid (or a gas, but this example uses a liquid) which is being heated at the bottom. The heated water at the bottom rises to the top and pushes cold water down. This water is then heated while the water at the top cools. This sets up a continual revolving motion while the water heats. On a molecular level, as the water at the bottom heats, the molecules move faster. This creates more space between them, and thus lower density water. This hot, less dense water is thus pushed to the top, and the colder, more dense water is heated at the bottom.

Radiation - Radiation is the transfer of heat when there is no medium (molecules) for it to travel through. It travels in the form of electromagnetic radiation (Infrared), and no molecule interactions are necessary.

3.3.8

Heat transmission through a solid occurs by the following equation:

$\displaystyle \frac{\Delta Q}{\Delta t} = \frac{-kA\Delta T}{\Delta x}$ .

Where $\frac{\Delta Q}{\Delta t}$ is the rate of heat flow, is a constant (negative to represent flow from hot to cold) related to the type of material. is the cross sectional area, is the temperature across the substance, and is the thickness.

This equation is in the data book, but it's fairly obvious that is would be proportional to area and temp diff, and inversely to thickness. If you need to calculate heat flowing through multiple media (ie through insulation then brick) then the equation becomes

$\displaystyle \frac{\Delta Q}{\Delta t} = A \times \frac{\Delta T}{(\frac{-x_1}{k_1} - \frac{x_2}{k_2})}$

ie, the total value for $\frac{k}{x}$ is the average for each material, weighted for relative thickness. That's not really in the course, but remembering it is easier than working it out. The first equation is in the data book.

3.3.9

The different thermal conductivities of different substances result from, firstly the availability of particles which are free to move. In metals, there are free moving electrons, able to flow, and thus carry heat more quickly than vibrations alone. Also, more dense substances tend to conduct heat more quickly, because the particles are closer and thus able to transfer kinetic energy between them.

3.4 Thermal properties of gases

3.4.1

Experiments to find the relationship between pressure, volume and temp

Pressure and volume ... Temp must be kept constant. This can be done by measuring the displacement in a movable tube manometer. The displacement adjusts the volume, and moves the mercury allowing the pressure to be measured (in cm of Hg) and then added to the air pressure (measured with a barometer). Thus allows values for both pressure and temperature to be found with no significant change in temperature. This relationship can then be graphed... Pressure will be inversely proportional to volume ... so a graph of pressure vs $\frac{1}{\mathrm{volume}}$ should be a straight line through the origin.

Pressure and temperature ... An enclosed glass 'bulb' of air should be connected to a manometer, and placed into a beaker. as the water in the beaker is heated, readings of both temperature, and pressure (as read from the manometer and a manometer. This allows a graph of temperature vs pressure...which should be a straight line through the origin.

Volume and Temp ... A capillary tube, sealed at one end, and bent upwards at the other, with a movable block of some kind (mercury) in the center. With the open end pointing up out of the water, dip the rest of the tube in a bath of hot water. Measure the position of the block, then cool the water with cold water, and then ice, measuring the temperature and volume at various points. This can then be graphed, giving a directly proportional relationship between volume and temperature (straight line through the origin ... intercept at -273c or 0 kelvin).

All these relationships fit PV = nRT if the appropriate variable is assumed to be constant.

3.4.2

$\displaystyle \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

This relationship, $\frac{PV}{T}$ is constant for a given number of molecules of gas, and for an ideal gas ... it is obviously related to PV = nRT .

3.4.3

As can be seen in the pressure vs Temp, and Volume vs temp graphs, the intercept on the temp axis is -273c. An ideal gas has no forces between the molecules, and that they have no volume. This means that the gas is compressible down to a point where pressure, or volume is zero. This point, obviously, is the absolute zero for temperature...which is -273c, or 0 kelvin.

3.4.4

$\displaystyle PV = nRT$ .

Pressure (Pa) x Volume (m³) = number of molecules (mols) x (a constant...8.31, in data book) x Temperature (in kelvin). Sub in numbers and solve for unknowns...

3.4.5

The definition of an ideal gas in microscopic terms ... A large number of point masses moving in random translational motion with no forces between them (and all collisions are completely elastic, and take no time). Temperature is defined as the the average kinetic energy of the molecules. Pressure is a result of the molecules colliding with the sides of the container, and 'bouncing' thus producing a force outward on the sides of the container.

3.4.6

The microscopic model of ideal gases can explain the macroscopic relationship between Temperature, Pressure and Volume. When temperature is increased, the molecules move faster. As a result, the rate of collision of the molecules with the sides of the container, and since the pressure is caused by the collisions, the pressure increases. If the volume is decreased (by pushing one side of the container in) the number of molecules per unit area increases. as a result, the rate of collisions increases, and so the pressure. Also, temp increases because, as the side is being pushed in, molecules are being given additional kinetic energy as they 'bounce off', because the speed they leave at is the speed they came in at + speed the side was moving...so many molecules gain a little bit of speed, increasing temp.