Thermodynamics

Pure Substance

Fixed, homogeneous chemical composition throughout

If we know P and T of a pure substance, we can determine:

• Phase

• Volume

• Enthalpy

• Entropy

Benefits of ideal gas law

• Easy to use

• Can be used for any gas

• Can be used on pure gases or mixtures

Disadvantages of ideal gas law

• Only accurate over a small T and P range

Principles of Corresponding States

"All fluids, when compared at the same Tr and Pr have approximately the same Z and all deviate from ideal gas behaviour" 

Pseudoreduced specific volume

General compressibility correlation for gases

2 methods of dealing with mixtures

• Dalton’s Law of Partial Pressures

• Amagat’s Law of Partial Volumes

Dalton’s Law of Partial Pressures

Total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases 

Amagat’s Law of Partial Volumes

Pure component volumes must add to give the total volume 

Partial Molar Properties

• TD properties which indicates how an extensive property changes with the molar composition 

• The partial derivative of the extensive property with respect to the number of moles 

Why do liquids tend to be less ideal than gases

• Slower movement

• Increases interactions

Enthalpy

A measure of total energy in a thermodynamic system

Energy

Measure of a capacity of a system to perform a change

Thermodynamic system

A system where energy is transferred, boundary that is defined

Why is using the change in enthalpy (dH) useful

It can actually be measured

Enthalpy change for endothermic

dH > 0

Enthalpy change for exothermic

dH < 0

Hess' Law

Change in enthalpy in a chemical reaction is independent of the pathway between the initial and final states

Method of measuring enthalpy change

Via calorimetry

Is Cp or Cv larger

Cp as heat goes to expansion work as well as temp change compared to Cv where volume is const

Do smaller or larger molecules have higher heat capacities

Larger molecules

Liquid-Gas

Vaporisation

Solid-Liquid

Fusion

Solid-Gas

Sublimation

For an ideal gas, enthalpy is:

• A function of temperature 

• Independent of pressure – even though PV is in the equation (use ideal gas to sub it in for nRT) 

For a non ideal gas, enthalpy is:

A function of pressure, e.g. supercritical water

At higher pressures, enthalpy is …. than the ideal value

Less

How can the non-ideal enthalpy change be found

Via generalised departure charts

Calculation steps for non-ideal enthalpy change

1) Ideal enthalpy change

2) Calculate Zh,1 using reduced pressure and temp 1

3) Calculate Zh,2 using reduced pressure and temp 2

4) Convert ideal enthalpy change to real using equation

Entropy

Measure of 'disorder' in a thermodynamic system (J/K)

Is entropy easy to calculate directly

No as its absolute value depends on microstates that are very hard to measure

Microstate

The number of possible ways that a system can exist in to give a specific result

Why do gases have higher entropies

They have a higher number of possible configurations, leading to more microstates

2nd Law of Thermodynamics

The total entropy change of an isolated system during a process always increases or, in the case of a reversible process, remains constant 

Why do most liquids have the same entropy of vaporisation

• There is a comparable amount of disorder generated when 1 mole of any liquid evaporates

• Around 85 J/K mol - Trouton’s Rule

Uses of entropy

• Efficiency is degraded by the presence of irreversible processes 

• Entropy generation is a measure of the magnitude of irreversibility present during the process 

What is the total entropy change when we have a change in T and P

Sum of the isothermal change and isobaric change

Assumes ideal gas

Why is entropy considered a state function

Steps can be done sequentially and in an order

How to work out entropy for non-ideal gases

• Entropy of departure charts are used (Zs)

• Similar to compressibility for non-ideal gases

Gibbs and spontaneity

• G < 0 = Spontaneous

• G = 0 = Neither forward nor backwards is favoured, equilibrium

• G > 0 = Non-Spontaneous

For Gibbs, if H is positive:

• Heat is removed from the surroundings 

• Endothermic 

• Need to rely on external energy transfer

For Gibbs, if H is negative:

• Heat is given to the surroundings 

• Exothermic 

For Gibbs, if S is positive:

• Local order decreased 

• Statistically more like outcome 

For Gibbs, if S is negative:

• Local order increased 

• Statistically less likely outcome 

3 requirements for thermodynamic equilibrium

1) It is in thermal eq (temp doesn't change with time or space) 

2) It is in mechanical eq (pressure doesn't change with time or space) 

3) It is in chemical eq (chemical potential does not change with time or space) 

How to find saturation pressure at constant T using steam tables

See where the volume dramatically decreases between pressure points, indicating a change in state

Chemical potential of components are …. at equilibrium

Equal

Potential indicates…

That the quantity is a driving force in the transfer of material from one phase to another

What does the Gibbs-Duhem equation show

Gibbs free energy of the system is equal to the sum of the chemical potentials

What are all derived thermo properties (U,H,G and A) functions of

V,P,S,T

Features of fugacity

• Derived from chemical potential to provide a measure of departure of a substance from its zero-pressure state 

• Measure of non-ideality of pressure 

• Analogous to compressibility for volume 

• For an non ideal gas, we can replace P with f for chemical potential calculations only 

What is the issue of calculating chemical potential for an ideal isothermal system

The potential tends towards negative infinity, which is not possible

Why can’t we solve the integrated form of Gibbs-Duhem for a non-ideal gas

Volume is a function of real pressure, hence a function of fugacity

How is pressure and fugacity related

Dimensionless fugacity coefficient

Where do we use fugacity

• At equilibrium, chemical potential change = 0  

• If the pressure is particularly high in a 2-phase system, estimations of partial pressures will be incorrect, as the chemical potential is non-ideal 

What ideal reference point is used for fugacity calculations

• Use steam tables

• Use a very low pressure (e.g. 0.01 bar)

What value of R do we use for these calculations

0.4615 kJ/kg K, to match other units