Thermodynamics

    Thermodynamics is the study of the conversion of energy into work and heat and its relation to marcroscopic variables such as temperature and pressure.

 

Arrhenius Equation

    Shows the dependence of the rate constant of chemical reactions on the absolute temperature and activation energy:

where
k - Rate constant                                E_a - Activation energy
A - Arrhenius constant                      R - Gas
e - Mathematical constant               T - temperature in Kelvin

 

Key concepts

• A system is classified as open, closed or isolated, adiabatic, diathermic
• The surroundings remain at constant temperature and either constant V or P when processes occur in the system
• Exothermic processes release heat, q to the surroundings. Endothermic processes absorb heat
• The work of expansion against constant external pressure Pext is:
• Maximum expansion work is achieved in a reversible change and the work is given by: 
  
• The change in internal energy is:
  
• Zeroth law states that 2 systems in thermal equilibrium with a third system are in equilibrim with each other

 

Laws of thermodynamics

   0. There is a unique scale of temperature

   1. The energy of an isolated system is constant

   2. When 2 systems are brought into thermal contact, heat flows spontaneously from the one at the higher temperature to the one at the lower temperature

OR

   2. Heat cannot be completely converted into work for any cyclic process, but work can be completely converted into heat

OR

   2. The entropy, S of an isolated system increases during any spontaneous change or process

   3. All perfect materials have the same entropy at absolute zero. It is impossible to cool any system to T = 0

 

States of Matter

i) Gas

• Behaviour - Fills the container it occupies
• Model - Is composed of widely separated particles in continuous rapid disordered motion. Each particle travels several diameters before colliding with another particle. The particles only interact weakly.

 ii) Liquid

• Behaviour - Processes a well defined surface. In a gravitational field it fills the lower part of its container
• Model - Is composed of particles in contact but able to move. Particles can only travel a fraction of a diameter before a collision occurs.

iii) Solid

• Behaviour - Retains its shape
• Model - Particles are in contact & unable to move past each other. Particles oscillate around an average location but are essentially trapped and frequently lie in more or less ordered arrays

 

Definitions

• Physical state - The condition of a sample of stuff in terms of physical form, volume, temperature, pressure and amount.
• Pressure - Fource per unit area
• Temperature - Determines the direction of energy flow
  
• Volume - The space occupied by a system, is an extensive property and a state function
  
• Energy - Capacity to do work
  
• Amount of stuff - Mole, 1mol is the number of particles in 12g of ¹²C
• Molar mass (mr) - Mass per mol of a substance
  
• Extensive property - Depends on amount, e.g. Mass, Volume
• Intensive property - Independent of amount e.g. Density, Concentration

 

Types of System

• Open - Energy and matter can be exchanged
• Closed - Only energy can be transferred as work or heat
• Isolated - Neither energy nor matter can be exchanged
• Adiabatic - Thermally isolated. Only work can be performed on or by the system
• Diathermic - Only heat can be exchanged between the system and its surroundings

 

Types of Work

Extension (f dl)	Volume (-Pext dV)
Surface (γ dσ)	Electrical (ϕ dq)

 i) Expansion of gas against a constant pressure:

ii) Isothermal reversible expansion

    Adjust pext to be equal to p at each infinitesimal step

    For an ideal gas, pV = nRT

iii) Irreversible expansion

    Instantaneously lower p_ext from p_A to p_B. The expansion ovvurs against constant external pressure p_B

    _{Therefore, for adiabatic or isothermal expansion}

    _{Heat transfer is different for the two different paths hance, not a state function}

_{where dU is an exact differential:}

_{where x and y are any two of p,V and T}

 

Quantifying heat changes

    Molar heat capacity - amount of energy required to raise 1 mol by 1K. Specific heat capacity is referred to 1g

i) Isochoric (constant volume) heat capacity, C_v
    If dV = 0, the system does no work

ii) Isobaric (constant pressure) heat capacity, C_p

where Cp depends on temperature, generally expressed as a poer series:

 

Enthalpy, H

    Hess's Law - The total enthalpy change for a reaction is independent of reaction path. The standard enthalypy of a reaction is the sum of the standard enthalpies of the individual reactions into which the reaction may be divided
Standard environment - 298K, 1atm

    Kirchoff's equation - shows the temperature dependence of 

where C_p(barred) is the mean heat capacity over the temperature range.

 

Entropy, S

    The amount of energy unavailable to do work which measures the disorder of a system

where k - Boltzmann constant

    For a reversible process

    Since

    The criterion for spontaneity is:

where H-TS is the Gibb's free energy, G the maximum amount of non-pV work that can be extracted from a system at constant p or V

    If the number of moles of different components vary:

 

Gibb's free energy

 

    Hence, the Gibbs-Helmoltz Equation

 

Free energy and equilibrium

    Le Chatelier's principle - perturbation of a system at equilibrium will cause the equilibrium position to change in such a way as to remove the perturbation.

 

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