Chapter 2 - The First Law

Basic concepts

• Thermodynamics - The study of the transformations of energy.
• Open system - Can exchange matter and energy with its surroundings.
• Closed system - can exchange energy with its surroundings, but not matter.
• Isolated system - No matter or energy is exchanged with the surroundings.

2.1 Work, heat, and energy

• Work - Motion against an opposing force.
• Energy - Capacity to do work.
• Heat - Energy change due to a temperature change between the system and its surroundings.
• Exothermic process - Process that releases energy as heat into its surroundings.
• Endothermic process - Process in which energy is obtained from the surroundings.

Molecular interpretation

• Thermal motion - Disorderly motion of molecules
  • Disorderly motion of molecules - It occurs due to heating.

2.2 The internal energy

• Internal energy - The total energy of a system, represented by U. It is the total kinetic and potential energy of molecules in the system.

  

• State function - A function where its value only depends on the current state of the system.

  • Internal energy is a state function and an extensive property.

• Internal energy, heat, and work can be measured in Joule (J), calories (cal), or kilocalories (kcal), but the most used one is Joule.

• 1 cal = 4.184 J

• First Law of Thermodynamics - The internal energy of an isolated system is constant.

  

2.3 Expansion work

• Expansion work - Work arising from a change in volume, whether it is positive (expansion) or negative (compression).

The general expression for work

When related to volume:

Free expansion

• Free expansion - Expansion against zero opposing force, when Pex = 0.
  • In free expansion, w = 0.

Expansion against constant pressure

Reversible expansion

• Reversible change - Change that can be reversed by any modification of a variable.

2.4 Heat transactions

Calorimetry

• Calorimetry - Study of heat transfer during chemical and physical processes.

• Calorimeter - Devise used for measuring energy transferred as heat.

• Adiabatic bomb calorimeter - Used to measure internal energy.

  

Heat capacity

• Heat capacity - The slope of the tangent to the curve at any temperature.

At constant volume, it’s defined as:

• Molar heat capacity at constant volume - The heat capacity per mole of material. It’s an intensive property.

  

• Specific heat capacity - The heat capacity of the sample divided by the mass.

  

So relating these equations with internal energy, we obtain:

Or:

2.5 Enthalpy

• Enthalpy (H), is defined as:

  

• Enthalpy is a state function.

Measurement of an enthalpy change

• Isobaric calorimeter - A calorimeter used for studying processes at constant pressure.
• Adiabatic flame calorimeter - Used to measure the temperature change in a combustion reaction.

Variation of enthalpy with temperature

• Heat capacity at constant pressure - The slope of the tangent to a plot of enthalpy against temperature at constant pressure.

  

Molar heat capacity at constant pressure - Heat capacity per mole of the material, it’s an intensive property.

Since enthalpy is the same as heat at constant pressure:

Thermochemistry

• Thermochemistry - Study of the energy transferred as heat during a chemical reaction.

2.7 Standard enthalpy changes

• Standard enthalpy change - The change in enthalpy for a process in which the initial and final substances are in their standard states.
  • Standard state - Pure form of a substance at a specified temperature and 1 bar.

Enthalpies of physical change

• Standard enthalpy of transition - Standard enthalpy change that accompanies a change of physical state.
• Standard enthalpy of vaporization - Enthalpy change per mole when a pure liquid at 1 bar vaporizes at 1 bar.
• Standard enthalpy of fusion - Standard enthalpy change accompanying the conversion of a solid to a liquid.

Enthalpies of chemical change

• Thermochemical equation - A combination of a chemical equation and the enthalpy change.

  

• Standard reaction enthalpy

  

• Standard enthalpy of combustion - Standard reaction enthalpy for the complete oxidation of an organic compound to CO2 gas and liquid H2O.

Hess’s Law

• Hess’s Law - The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.

2.8 Standard enthalpies of formation

• Standard enthalpy of formation - Standard reaction enthalpy for the formation of the compound from its elements in their reference states.
• Reference state - The most stable state of an element at the specified temperature and 1 bar.

Reaction enthalpy of enthalpies of formation

Enthalpy of formation and molecular modeling

• Mean bond enthalpies - Average enthalpy change associated with the breaking of a specific A--B bond.

2.9 Temperature dependence of reaction enthalpies

• Kirchhoff’s Law

  

State functions and exact differentials

• Path functions - Processes that describe the preparation of the state.

2.10 Exact and inexact differentials

• Exact differential - An infinitesimal quantity that, when integrated, gives a result that is independent of the path between the initial and final states.
• Inexact differential - An infinitesimal quantity that, when integrated, gives a result that depends on the path between the initial and final states.

2.11 Changes in internal energy

General considerations

When V changes to V + dV at constant temperature, U changes to

• Internal pressure

  

Changes in internal energy at constant pressure

• Expansion coefficient - The slope of the plot of volume against temperature at constant pressure.

  

• Isothermal compressibility - Measure of the fractional change in volume when the pressure is increased by a small amount.

  

2.12 The Joule-Thomson effect

• Joule-Thomson coefficient (µ)

  

• Isenthalpic expansion - Expansion at constant enthalpy.

• Joule- Thomson effect - Cooling by isenthalpic expansion.

• Isothermal Joule- Thomson coefficient

  

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