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IBH Thermal Physics Notes (6 hours)

 Absolute zeroConsider a quantity of gas in a container of variable volume. If we change the temperature of the gas and allow it to change volume at constant pressure, the results are as shown by thegraph below

Extrapolating backwards we find the graph crosses the x axis at -273°C.

This suggests that the volume occupied by the gas because of the motion of its molecules would be zero at -273°C. This suggests that this is the lowest temperature possible.

Note that the absolute zero of temperature has not been attained in practice; it is atheoretical prediction found by extrapolation of experimental results.

The Macroscopic Gas laws 

• For a fixed amount of gas at constant temperature, pressure × volume = constant.(pV = constant)

• For a fixed amount of gas at constant pressure, volume/temperature = constant.(V/T = constant)

• For a fixed amount of gas at constant volume, pressure/temperature = constant.(p/T = constant)

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Use this information to sketch the following graphs

Constant volume Constant temperature

PressurePressure

Temperature Volume

1/Volume

Constant temperature

Pressure

Temperature

Volume

Constant pressure

Ideal gas equationThe equation of state of an ideal gas ties the three macroscopic gas laws together.The equation of state of an ideal gas is

pV nRT=  

where n is the number of moles of gas and R is the universal molar gas constant (look it upin your data booklet).

The units of pressure are Pascals (one Pascal is one Newton per meter squared)The units of volume are meters cubed (1 m

3= 1000 litres)

The units of temperature are Kelvin (you have been warned!)

For before and after comparison questions where the amount of gas is constant 1 1 2 2

1 2

p v p v

T T=  

holds. Non-standard units may be used here as long as they areconsistent (you must use Kelvin however)

 A Thermodynamic System  A Thermodynamic System is that part of the universe that is under 

consideration. A real or imaginary boundary separates the system fromthe rest of the universe, which is referred to as the environment or surroundings (sometimes called a reservoir.). A system can be anything,for example a piston, a solution in a test tube, a living organism, or a

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planet.

WorkWork is done when a force moves a distance in the direction of the force. Consider thecompression of the gas by the piston below. Work is done on the gas and this increases it’sinternal energy, if the system is not isolated from it’s surroundings heat will flow out from thepiston

Consider the expansion of the gas below. Heat flows into the system increasing the internalenergy of the gas, the gas does work on its surroundings.

These concepts are expressed in the first law of thermodynamics.

The first law of thermodynamics states that the thermal energy transferred to a gas is equalto the sum of the internal energy increase and the work done by the gas.

Q U WΔ = Δ + Δ  

Where +ΔQ = thermal energy transferred to the system

Where +ΔU = the increase in internal energy of the system

Where +ΔW = work done by the system

The first law of thermodynamics is a statement of the principle of energy conservation.

The work done by a volume change of a gas at constant pressureConsider a quantity of gas in a container which has a frictionless piston as shown in the

diagram below. The volume occupied by the gas is changed by ΔV.

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The pressure, p, acting on the surface of the piston produces a force, F, equal to PA. Duringthe change in volume, this force does some work.The work done by this force is w = Fs = PAs

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

W = PΔV

p-V Diagrams A "p-V diagram" is a graph showing changes in the pressure and volume of a sample of gas.It is useful to be able to recognise various types of change of the state of a gas from a p-Vdiagram. Four examples are given below.

1. Change of p (and T) at constantvolume; an isovolumetric (also calledisochoric) change.2. Change of V (and T) at constantpressure; 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); anadiabatic change.

In practice, changes of state do not quite follow any of these ideal paths. However,approximate isothermal, adiabatic etc changes can occur.In practice:

• for an isovolumetric change, heat the gas in a fixed volume container (one made of amaterial having a low thermal expansivity)

• for an isobaric change, trap a small quantity of the gas in a tube using a thread of mercury and heat it slowly 

• for an isothermal change, compress (or expand) the gas slowly in a container of  highthermal conductivity

• for an adiabatic change, compress (or expand) the gas rapidly in a container of  lowthermal conductivity.

On a p-V diagram, an isothermal looks like an adiabatic. However, if an isothermal and anadiabatic have a point in common, then the adiabatic is the curve having the greater slope atthat point.

p-V Diagram for the Carnot CycleThe Carnot cycle can be represented on a graph of pressure against volume (a p-V diagram)as shown below.

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 D to A isothermal expansion at T1; work done by the gas

 A to B adiabatic expansion; work done by the gasB to C isothermal compression at T2; work done on the gasC to D adiabatic compression; work done on the gasThe product of pressure and volume represents a quantity of work (see the section "WorkDone During a Change of Volume of a Gas"). This is represented by the area below a p-Vcurve.Therefore, the area enclosed by the four curves represents the net work done by the engineduring one cycle.

The Second Law Of Thermodynamics The Second Law Of Thermodynamics states that

“Heat cannot spontaneously flow from a material at lower temperature to a material at higher temperature.”

EntropyEntropy is a property of a system that expresses the degree of disorder in the system. A more general statement of the second law of thermodynamics is“The entropy of an isolated system never decreases.”Think of the bounce of a squash ball. As the ball heads towards the floor all its particles areheading in the same direction with similar kinetic energies, this a highly ordered system. After the bouncing stops particles in the system (ball, air and floor) have increased heatenergy. This is a degraded, lower quality form of energy and is more disordered. The originalhighly order state, the falling ball cannot be recovered from this heat energy. There aremany examples of this, the falling down of buildings, a smashed glass of water does notreassemble itself etc. This will inevitably lead to the “heat death of the universe” as highlyordered states of energy (stars) spread into more degraded forms of energy.What would the second law have to say about the growth of a tree? Or the cooling of afridge?