Thermal Physics HL

Assumptions of the kinetic theory

1. Molecules behave as if they were hard, smooth, elastic spheres. (i.e. the collisions are perfectly elastic)

2. Molecules are in continuous rapid, random motion.3. The average kinetic energy of the molecules is

proportional to the absolute temperature of the gas.4. The molecules do not exert any appreciable

attraction on each other.5. The volume of the molecules is infinitesimal when

compared with the volume of the gas.6. The time spent in collisions is small compared with

the time between collisions.

Pressure and temperatureGay-Lussac’s Law

As the temperature is reduced, the pressure decreases (Why?)

If the graph is extrapolated, then the intercept gives the value of absolute zero These results do not depend on the type of gas.

P1 / T1 = P2 / T2

Pressure and volume

Take measurements of pressure and volume

Plot a suitable graph to determine the relationship between these 2 variables.

Boyles’ Law

Boyle’s Law

The pressure of a fixed mass of gas at constant temperature is inversely proportional to the volume.

p1V1 = p2V2

Boyle’s Law animation

Charles’ Law

The pressure of a fixed mass of gas at constant volume is directly proportional to the absolute temperature.

                        

Hyperlink

Charles’ Law animation

Equation of state for an ideal gas

Combining the previous gas laws gives

Therefore, for 1 mole of an ideal gas;

PV = (a constant)×T

PV = nRTP = Pressure V = Volume

n = number of moles

R = Universal gas constant

T = Temperature (KELVIN)

Gas equation animation

Click on image to activate pV = nRT

Gas properties simulation

Describe the concept of the absolutezero of temperature and the Kelvin

scale of temperature.

Questions1. A diver exhales a bubble of volume

2cm3 at a depth of 30m (Pressure = 4 Atmos). What is the volume of the bubble when it reaches the surface? (Isothermal). (8)

2. A fixed volume of gas is heated from 100kPa at 270C to 350kPa. What is it’s new temperature? (777)

3. A sample of Neon gas occupies a volume of 45 litres at 100kPa and 200C. How many moles of gas are there? (1.85)

A-level Q’s 1a,2,3,5a(i),6a,6b(i),7(a),8(a)(b)(c),9,10(a),11(a),13

Tsokos

Page 181 Q’s 1- 9.

Ideal Gases and Real Gases

• Real gases behave as ideal gases at room temp and pressure.

• The gas molecules become “interacting” at high temperatures and high pressures. Therefore they lose there ideal properties.

• Ideal gases cannot be liquefied.

• Ideal gases obey the gas equation.

Work done in compressing a gas

The work done by this force is w = Fs = PAs, since F=PA

but As is the change in the volume occupied by the gas, ΔV. therefore;

W = PV

Deduce an expression for the work involved in a volume change of a gas at constant pressure.

Conservation of energy

If we add energy to a fixed mass of gas, the gas will increase in temperature (internal energy ΔU).

ΔU =

1st Law of Thermodynamics

We can add energy by heating (temperature gradient) = Q

Or by working (no temperature difference) = W

Q = ΔU + WQ = Heat energy added to the gas

ΔU = Temperature increase of the gas

W = Work done by the gas.

State the first law of thermodynamics.

Students should be familiar with the terms system and surroundings. They should also appreciate that if a system and its surroundings are at different temperatures and the system undergoes a process, the energy transferred by non-mechanical means to or from the system is referred to as thermal energy (heat).

1st Law questions

• 1b

• 10(a),(c),(dii)

• Tsokos page 193 Q’s 1

Q = ΔU +W

W

Q

ΔU

P-V changes

                                                               

                  

1. Change of p (and T) at constant volume; an isovolumetric change.2. Change of V (and T) at constant pressure; an isobaric change.3. Change in p and V at constant temperature; an isothermal change.4. Change in p and V in an insulated container (no heating of the gas); an adiabatic change.

Isothermal gas processes

For a fixed mass and temperature of gas, state the values of Q, ΔU and W as the gas expands.

Isothermal P-V changes

Q =

ΔU =

W =

Isochoric changes (Volume)

Isochoric changes

Q =

ΔU =

W =

Isobaric changes (Pressure)

Isobaric changes Q =

ΔU =

W =

Adiabatic changes

Q =

ΔU =

W =

Adiabatic changes

These are defined as processes where no heat can flow in or out of the system. This occurs when the change happens too rapidly for the heat to be exchanged. Therefore they result in a change in temperature of the gas

Ideal gas processes

Isobaric process: pressure constant V/T constant

Isochoric process: volume constant p/T constant

Isothermal process: temperature constant pV constant

Hyperlinkhttp://www.walter-fendt.de/ph14e/gaslaw.htm

Conservation of energy for Carnot cycle

                

                                                                                                         

Curve AIsothermal

expansion at TH

 Work done by the

gas

Curve B Adiabatic expansion

 Work done by the

gas

Curve CIsothermal

compression at TC

 Work done on the

gas

Curve DAdiabatic

compression

 Work done on the

gas

For each part of the cycle, findQ = ?ΔU = ?W = ?

Otto cycle

Click to play

Carnot cycle

How does energy enter and leave the gas in a Carnot cycle?

Picture has a hyperlink

Work done in a thermodynamic process

The product of pressure and volume represents a quantity of work. This is represented by the area below a p-V curve.Therefore, the area enclosed by the four curves represents the net work done by the engine during one cycle.

                     

                                                                                                

    

Tsokos

Page 193 Q’s 2-5

Second Law: Entropy a measure of the amount of energy which is unavailable to do work

a measure of the disorder (of the energy) of a system

How “useful” is the energy? Which can do the most work for us? 100j of energy in petrol or 100j of energy as heat? The heat is “disordered” or “higher entropy”

Every time we change energy from one form to another, we increase the entropy of the Universe.

Second Law of Thermodynamics

The second law of thermodynamics is a general principle which places constraints upon the direction of heat transfer and the attainable efficiencies of heat engines. In so doing, it goes beyond the limitations imposed by the first law of thermodynamics. It's implications may be visualized in terms of the waterfall analogy.

Second Law: Heat Engines Second Law of Thermodynamics: It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W . Some amount of heat QC must be exhausted to a cold reservoir. This precludes a perfect heat engine.

Second Law: Refrigerator Second Law of Thermodynamics: It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object. This precludes a perfect refrigerator. The statements about refrigerators apply to air conditioners and heat pumps, which embody the same principles.

Tsokos

Page 194 Q’s 9-13.