Gas Laws and Pure Substances

MEE1018: Thermodynamics and Fluid Mechanics - Lecture 2

Temperature

It is a measure of ‘how hot’ or ‘how cold’ something is relative to some reference point.

Temperature difference

The potential to produce heat flow (like voltage). Heat will flow naturally from higher temperature to lower temperature.

Thermal equilibrium

When two objects have the same temperature.

Zeroth Law of Thermodynamics

When two objects are separately in thermodynamic equilibrium with a third object, they are in equilibrium with each other.

Uses of Zeroth Law

Used to calibrate a thermometer by putting the thermometer in thermal equilibrium with a known physical system at several reference points. (e.g. freezing and boiling point of water).

Fahrenheit scale

0F = Freezing point of salt / ice

100F = Body temperature

Celsius scale

0C = Freezing point of water

100C = Boiling point of water

Celsius and Fahrenheit conversion

The gas thermometer

If pressure times volumes is plotted against temperature for any gas is a straight line.

Relationship between temperature and pressure of a gas in a vessel

T = a +bP, where a and b are constants determined experimentally.

Kelvin scale

0 = The lowest theoretical temperature possible. Also called the absolute scale.

Use of Kelvin scale

When doing absolute temperature measurements or taking ratios

Kelvin, Celsius Conversion

T(K) = T(°C) + 273.15

Scale used when measuring temperature differences ΔT

Kelvin or Celsius

Latent heat

The amount of energy absorbed or released during a complete phase change.

Latent heat of fusion

The energy input required to completely melt a solid.

Latent heat of vapourisation

The energy input needed to completely vapourise a fluid.

Gas variables

p: pressure, V: volume, T: temperature, n: moles or m: mass

To investigate the relationship between 2 gas variables

We need to hold the other 2 constants.

Constant p - same number of collisions / unit area (frictionless piston in vertical cylinder).

Constant V - rigid container.

Constant T - thermostat control

Constant n or m - keep container sealed.

Boyle’s Law

The pressure of a gas is inversely proportional to its volume.

p ∝ 1/V pV = C p₁V₁ = p₂V₂

Charles’ Law

When the pressure of a gas is constant, the volume will be directly proportional to temperature on the Kelvin scale.

V ∝ T V/T = C V₁/T₁ = V₂/T₂

Amonton’s Law / Gay Lussac’s Law

The ratio between the volumes of the reactant gases and the gaseous products can be expressed in simple whole numbers.

p ∝ T p/T = C p₁/T₁ = p₂/T₂

Avogadro’s Law

Equal volumes of gases have equal numbers of molecules at equal temperature and pressure.

V ∝ n V/n = C V₁/n₁ = V₂/n₂

Ideal gas equation

pV = nR₀T, where R₀ is the universal gas constant

pV = mRT

Individual gas constant

Unique to each particular gas

Individual gas constant equation

R = R₀/M

Other useful forms of the universal gas equation

p = ρRT

pv = RT

Pure substance

A substance that has a fixed chemical composition throughout.

Pure substance examples

Nitrogen and gaseous air

A pure substance in more than one phase

A pure substance may exist in more than one phase, if the chemical composition is the same in all phases.

Compressed liquid

A liquid well below boiling point.

Saturated liquid

A liquid that is ready to vapourise.

Saturated liquid-vapour mixture

Part of the saturated liquid is vapourised.

Saturated vapour

The temperature remains constant until the last drop of liquid is vapourised.

Superheated vapour

The temperature of the vapour starts to rise.

T-V graph of a pahse chage processes of pure substances

Water at atmospheric pressure

Saturation temperature, T_sat

The temperature at which a pure substance changes phase at a given pressure.

Saturation pressure, P_sat

The pressure at which a pure substance changes phase at a given temperature.

T-V Isobars at different pressures

As pressure increases

• Boiling point (saturation temperature) increases

• Specific volume of saturated vapour decreases.

The flat regions of the isobars correspond to states for which vapour and liquid coexist, i.e. there is a mixture of gas and liquid.

Critical point

The point of inflexion on a t-v graph,

Reading a phase change process diagram

Inside the dome - liquid and vapour present (saturated mixture)

To the left of dome - only liquid present (compressed liquid region)

To the right of dome - only vapour present (superheated vapour / gas region)

Above the critical point - supercritical isobars

Supercritical isobars

Isobars above the critical point.

Supercritical fluid

A material that has properties intermediate between a liquid and a gas. S

Triple point

A point where all three phases coexist (solid, liquid and gas).

Triple point pressure and temperature

A substance exists in three phases in equilibrium (all states at same temperature and pressure, but different specific volumes).

Sublimation

The process in which, below the triple point pressure solids will not melt, i.e. there is no liquid phase, but instead will pass directly from a liquid to a solid.