Thermodynamics Lecture - 05

First Law of Thermodynamics

• Definition: Conservation of energy. Energy cannot be created or destroyed but can be transformed from one form to another.
• Equation: ( \Delta U = \Delta Q + \Delta W )
  • ( \Delta U ): Change in internal energy
  • ( \Delta Q ): Heat added to the system
  • ( \Delta W ): Work done on the system

Concepts

• Internal Energy (U)

  • Sum of kinetic and potential energies of molecules.
  • For ideal gases, internal energy depends only on temperature.
  • Kinetic Energy: Due to translational, vibrational, and rotational motion of molecules.
  • Potential Energy: Due to molecular interactions.
  • Properties: Extensive property and a state function.

• Heat (Q)

  • Form of energy exchange.
  • Positive: When heat is given to the system.
  • Negative: When heat is given by the system.
  • Formula: ( Q = nC\Delta T )
    • ( C ): Specific heat capacity, varies with process (( C_P, C_V )).

• Work (W)

  • Energy transfer due to volume change.
  • Positive: Work done on the system.
  • Negative: Work done by the system.
  • Formula: For gases, ( W = -P_{ext} \Delta V ) or area under the PV curve.

Processes

• Isothermal: Constant temperature, ( \Delta U = 0 ).
• Isobaric: Constant pressure, use ( C_P ).
• Isochoric/Isovolumetric: Constant volume, ( W = 0 ).
• Cyclic: ( \Delta U = 0 ), use area under PV curve to find work.

Calculations

• Internal Energy Change: ( \Delta U = nC_V \Delta T ) (for ideal gases)
• Molar Specific Heat Capacities: ( C_V ) for constant volume, ( C_P = C_V + R ) for constant pressure.
• Degrees of Freedom
  • Monatomic: 3
  • Diatomic: 5
  • Polyatomic: 6

Problem Solving

• For given processes, apply the first law to solve for unknowns using known quantities.
• Assess whether processes are isothermal, isobaric, or cyclic to determine relevant equations and relationships.