Thermal Physics

Thermal Physics

The Kinetic ModelAssumptions: Matter is made up of tiny particles Particles are always moving The spacing of the particles The ordering of the atoms The motion of the atoms Solid: small spacing, well ordered lattice, no motion except lattice vibrationLiquid: small spacing with some gaps, less well ordered, motion fairly slowGas: large spacing, no order, fast and randomAtoms of gasAtoms of a gas are fast moving, bouncing off walls of container and each other as they travel around at high speed. They also move around in a disordered way.

Brownian motion and evidence for the movement of molecules:The smoke cell contains air into which a small amount of smoke has been let in. The cell is lit from the side, and the microscope is used to view to view the smoke grains.The smoke grains move randomly and fast because of collisions with the air molecules.This provides evidence that the air molecules must be moving and have haphazard motion.Little side note: This experiment is carried out because air molecules are too small to see, so we look at the smoke particles as they are bigger and let us see the effect of the air molecules

Show that, since M>>m, it follows that air molecules must be moving much faster than the smoke grain (V>>v).1/2 mv^2 = 1/2MV^2v/V=√M/m since M>m it follows that v >VFast moleculesThe average speed of air molecules at standard temp and pressure, is about 400m/s, but some move faster or slower than this . For example, if you followed the movement of a single air particle, some of the time you would observe its speed being below or above the average speed some times.The velocity of an individual air molecule changes every time it collides with something else.Explaining pressureA gas exerts pressure on any surface it contacts. Pressure (the force per unit area).

Thermal Physics

Consider a molecule of mass m travelling at right angles towards the wall of a container at speed v. It makes an elastic collision with the wall and rebounds at speed v. This impact exerts a force F on the wall. Using Newton's second law:F=rate of change of momentum (of molecule)F=Δp/ΔtΔp=final momentum - initial momentumΔp= (-mv) - mv = -2mvTherefore: F= -2mv/Δt (negative sign means the force exerted on the molecule by the wall is in opposite direction to initial velocity)A large number of molecules make the same collisions with the wall, resulting in a large total force on the wall.To find pressure exerted on wall from mol collisions:pressure= total force/area of wall

Changes of state

Consider first what happens when a solid is heated and melts, the atoms of the solid gain enough energy to break some of the bonds with their neighbours. So they become more disordered and the their (average) spacing increases.The atoms are more free to move around - the solid has melted.As the liquid is heated further, the atoms become more disordered, their spacing increases further and they become faster moving. Eventually at boiling point, the atoms have enough energy to break free from their neighbours. Now they are much more further apart, moving very fast in a disordered state - the liquid has boiled to become a gas.The kinetic model is useful, but doesn't explain everything, for example, the change in density of ice when it melts.Our model suggests that, when a solid melts, the particles become more disordered and further apart (on average). So this would suggest that the liquid is less dense than the solid. (This is generally the case but there are exceptions). Ice is less dense than water.

We therefore have to modify the model, for water we picture the molecules as not being spherical. When the liquid water becomes solid ice, the particles pack in way so there is more empty space, so the solid is less dense than the liquid.http://49.media.tumblr.com/e4a282dc44287d5e36d36cd85e968308/tumblr_mv2z1etolW1sjwwzso1_500.gifHeating iceImagine taking some ice from deep freeze, and putting it in a insulated container and heating it. It's temperature will rise; eventually we will have a container of steam (steam is a cloud of tiny droplets of liquid water - not gas!).Energy is supplied to the ice at a constant rate, we will consider the different stages of the graph. We need to think about kinetic and potential energies of the molecules.If the molecules move around more freely and faster, their kinetic energy has increased.If they break free of their neighbours and become more disordered, their electrical potential energy has increased.

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Caption: : Temperature against time graph for ice, heated at a steady rate.

Section AB - The ice starts below 0°C, its temperature rises. The molecules gain energy and vibrate more. Their kinetic energy is increasing, but there is little change in the molecules avg separation so there is little change in their electrical potential energy.Section BC - The ice melts at 0°C. The molecules become more disordered, separation of the molecules increases so their electrical potential energy increases.Section CD - The ice has become water. Its temperature rises toward 100°C. The molecules move more sotheir KE increases. There is little change in the mean separation of the molecules so there is little change in their electrical potential energy.Section DE - The water is boiling, the molecules are becoming completely separate from their neighbours. There is a large increase the the separation of the molecules so their electrical potential energy has increase greatly.Section EF - The steam is being heated above 100°C. The molecules move even faster, their KE is increasing. The molecules have max electrical potential energy of zero

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From this analysis, you can see that when water is heated it involves the following (when its flat BC and DE): there must be an input of energy the temperature doesn't change the molecules are breaking free from their neighbours their potential energy is increasing In between the changes of state (when its increasing): the input of energy raises the temperature of the substance the molecules move faster (so their KE increases) The energy which must be supplied to cause a change of state is sometimes  called 'latent heat'. When a substance melts, it's called the latent heat of fusion.When a substance boils, it is the latent head of vaporisation.

Latent heat of fusion is the energy which must be supplied to cause a substance to melt at constant temperature.Latent heat of vaporisation is the energy which must be supplied to cause a substance to boil at constant temperature.If they break free of their neighbours and become more disordered, their electrical potential energy has increased.

Evaporation

When you melt something, its temperature does not rise. Also a note that melting takes less energy than boiling as with boiling you are completely separating the atoms and this takes up more energy - breaking more bonds.EvaporationA puddle of rain water dries up without having to be heated to 100 C. When a liquid changes to gas without boiling , we call this evaporation. The gas formed is vapour - gas below its boiling point.Within the liquid molecules are moving about, some  move faster than others, and can break free from the liquid.They form the vapour above the liquid.Some molecules from the vapour may come back into contact with the liquid, and return to the liquid. But since there is a net flow of energetic molecules from the liquid, it will evaporate away completely eventually

When a liquid evaporates, the particles with the most energy escape. When you're wet, you get cold because:water will evaporate from your skin. The most energetic molecules escape, leaving behind the slower moving ones. So the average KE of the water on your skin decreases, make it a lower temperature, (because avg speed or KE of particles is temperature).What increases rate of evaporation: Put it in a warmer place, higher temp means more particles are moving fast enough to escape. Increase surface area so more particles can escape from the surface. Less moisture in the air, because if there is moisture in the air the vapour will become liquid after coming into contact with the surface of the liquid.

INTERNAL ENERGY

General principle with example of stone, to increase the energy of the stone, we could heat it. The energy seems to have disappeared into the stone as KE or GPE of stone doesn't change. As stone gets hotter, the electrical potential energy and kinetic energy of the stone increases because the molecules vibrate faster and more (KE) and they get separate further (PE).This energy of the molecules is known as the internal energy of the stone:The internal energy of a system is the sum of the random distribution of kinetic and potential energies of its atoms or molecules.Molecular EnergyChanging internal energy - two ways to increase internal energy of a gas; heat it or do work on it by compressing it Heating a gas - walls of container get hotter so the molecules get hotter and so vibrate faster and more, they collide faster and so gain kinetic energy - temp increases. Doing work on the gas - wall if container is pushed inwards so molecules bounce off faster. They gain KE and so the temperature has risen.

The meaning of temperatureEnergy flowing from a region of higher temperature to a region of lower temperature is called thermal energy.Thermometer in water example.When two objects are in contact and are at the same temperature and there is no transfer of thermal energy between them - thermal equilibrium.Thermodynamic (Kelvin) scaleIt is not possible to have a temperature lower than 0K (absolute zero). For any matter at absolute zero, you can't remove any more energy from it. Absolute zero is the temperature at which all substances have minimum internal energy (the KE and electrical potential energy of the particles is minimum).T (K) = θ (°C) + 273θ (°C) = T (K) - 273Thermodynamic scale fixed points: absolute zero - 0K triple point - temperature at which water, ice and water vapour can coexist at 273K

Calculating energy changes

amount of energy needed to change temperature of somethingSpecific heat capacityIf we heat something so its temperature rises, amaount of energy we must supply depends on three things: mass, m, of the material ur heating temperature change, Δθ, you want the material itself, as different materials have different specific heat capacities E=mcΔθ so c=E/mΔθSpecific heat capacity = energy supplied/mass x temperature change

Experiment to determine the specific heat capacity of a solid and liquid:For solid, a metal cylinder of mass 1kg heated by an electrical heater, wrapped in insulator and with a digital thermometer to record temperature change.For liquid, liquid of known mass  with insulating lid, and heating coil, and the liquid is also wrapped in an insulator and has a digital thermometer to record temperature change. Heat the substance with the heater to get a certain temperature rise. With an ammeter and voltmeter connected to the heater, calculate the energy supplied using E=IxVxΔt (energy =currentxvoltage=time remember P=IV) Plug your data into E=mcΔθ to calculate c Sources of error: some of the energy will escape to the surrounding even though its wrapped in insulating material low rate of heating so temperature spreads out

Specific latent heat

The specific latent heat of a substance is the energy required per kilogram of the substance to change its state without any change in temperature.when substance melts - specific latent heat of fusionwhen it boils - specific latent heat of vaporisation