Thermodynamics: First Law and Internal Energy Concepts

The First Law of Thermodynamics: There is No Free Lunch

Overview of the First Law of Thermodynamics

  • Also known as the Law of Conservation of Energy.
  • States that energy is neither created nor destroyed in chemical processes.
  • The total energy of the universe remains constant; thus, the change in energy of the universe is zero.

Internal Energy (E or U)

  • Defined as the sum of all kinetic and potential energy within a system.
  • Internal Energy is a state function, meaning:
    • The value of Internal Energy depends on the state of the system (e.g., temperature, pressure, concentration, and phase) but not on how the system arrived at that state.

State Function

  • A variable or value that depends only on the current state of the system, not the path taken to reach that state.
    • Example: Elevation is a state function, as it is independent of the trajectory taken to reach that altitude.

Calculation of Changes in Internal Energy

  • Measuring the internal energy (E) directly can be difficult; instead, the change in internal energy (ΔE) is measured.
  • Example: For the reaction of carbon and oxygen to form carbon dioxide:
    • Reactants: C (s) + O₂ (g)
    • Products: CO₂ (g)
    • Measured energies:
    • E_reactant: 800 kJ
    • ΔE = Eproduct - Ereactant
Example Calculations

  • First Case:

    • E_product = 400 kJ
    • ΔE = 400 kJ - 800 kJ = -400 kJ

  • Second Case:

    • E_product = 550 kJ
    • ΔE = 550 kJ - 950 kJ = -400 kJ

Implications of the First Law

  • According to the first law, energy lost by a system equals the energy gained by the surroundings, and vice versa.
    • If energy cannot be created or destroyed:
    • Energy lost by the system = Energy gained by the surroundings
    • Energy gained by the system = Energy lost by the surroundings

Changes in Internal Energy ( \Delta E )

  • Changes in internal energy can occur through:
    1. Heat (q)
      • +q: the system absorbs heat.
      • -q: the system releases heat.
    2. Work (w)
      • +w: work is done on the system.
      • -w: work is done by the system.
  • Note: q and w are not state functions; their values depend on the process and conditions under which the state change occurs.

Example Problem

- A system receives 425 J of heat and delivers 425 J of work to its surroundings. Determine the change in internal energy.

  • Heat received, q = +425 J
  • Work done, w = -425 J
  • Since both increase and decrease cancel each other out:
    • ( \Delta E = q + w = 425 J - 425 J = 0 J )