Assumptions of the kinetic theory
1. Molecules behave as if they were hard, smooth,
elastic spheres. (i.e. the collisions are perfectly
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 temperature
P1 / T1 = P2 / T2
As the temperature is reduced,
the pressure decreases (Why?)
If the graph is extrapolated,
then the intercept gives the
These results do not depend on the type of gas.
value of absolute zero
Pressure and volume
Take measurements of pressure and volume
Plot a suitable graph to determine the relationship
between these 2 variables.
The pressure of a fixed mass of gas at constant temperature is inversely proportional
to the volume.
p1V1 = p2V2
Equation of state for an ideal gas
Combining the previous gas laws gives
PV = (a constant)×T
Therefore, for 1 mole of an ideal gas;
P = Pressure
PV = nRT
V = Volume
n = number of moles
R = Universal gas constant
T = Temperature (KELVIN)
Gas equation animation
Click on image to activate
pV = nRT
Describe the concept of the absolute
zero of temperature and the Kelvin
scale of temperature.
1. 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?
2. A fixed volume of gas is heated from 100kPa at 27 0C 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
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
Deduce an expression for the
work involved in a volume change
of a gas at constant pressure.
The work done by this force is w = Fs = PAs,
but As is the change in the volume occupied by the gas, ΔV.
W = P∆V
Conservation of energy
If we add energy to a fixed mass of gas, the gas
will increase in temperature (internal energy ΔU).
1 Law of Thermodynamics
State the first law of thermodynamics.
We can add energy by heating (temperature
gradient) = Q
Or by working (no temperature difference) = W
Students should be familiar with
the terms system and
surroundings. They should also
Q = Heat energy added to the gas appreciate that if a system and
its surroundings are at different
ΔU = Temperature increase of the temperaturesprocess, system
energy transferred by nonmechanical means to or from
the system is referred to as
W = Work done by the gas.
thermal energy (heat).
Q = ΔU + W
1 Law questions
• Tsokos page
193 Q’s 1
Q = ΔU +W
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
Isothermal gas processes
For a fixed mass and temperature of gas, state the values
of Q, ΔU and W as the gas expands.
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
Conservation of energy for Carnot cycle
expansion at TH
Work done by the
Work done by the
Work done on the
For each part of the cycle, find
ΔU = ?
Work done on the
Picture has a hyperlink
How does energy enter and leave the
gas in a Carnot cycle?
Work done in a thermodynamic
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.
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
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
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.