In-Depth Thermodynamics Notes

Definition of Balances
  • All extensive properties should be conserved according to the principles of thermodynamics.
  • For property X: Differentiation in time (division by dt) gives rates.
  • Example: Energy is measured in Joules, whereas Power is measured in Watts.
Practical Use of Energy Balance
Calculation of Stored Energy
  • For most first law analyses, calculating the change in energy (ΔE) is essential.
  • Equation: ΔE = ΔU + ΔKE + ΔPE
    • For stationary systems: ΔKE = ΔPE = 0.
  • In general:
    • 2KE = (1/2)m(V² - V₁²)
    • ΔPE = mg(h₂ - h₁)
  • Methods to calculate ΔU:
    1. Reference thermodynamic tables for u₁ and u₂ (e.g. states of water).
    2. Relate ΔU to ΔT using specific heat capacities (Cp and Cv).
1st Law of Thermodynamics
  • The first law states that total energy of a system changes in relation to heat and work interactions.
  • For closed systems (control-mass), rate terms will follow:
    • Energy entering - Energy leaving = Change of energy within the system
    • Heat Transfer: Positive when heat enters the system, negative when it leaves.
    • Work Transfer: Positive when work is done by the system, negative when work is done on the system.
Nature of Energy Interactions (Work)
  • Work can be conceptualized as raising or lowering a weight.
  • Types of Mechanical Work:
    1. Work due to moving boundaries.
    2. Electrical work entering the system (considered potential).
Moving Boundary Work
  • The work done during volume changes can be represented as:
    • W = ∫ P dV (where A is the piston's cross-sectional area)
  • Process Types:
    • Compression is positive work; Expansion is negative work.
  • Different kinds of processes include:
    1. Isobaric (Constant Pressure)
    2. Isothermal (Constant Temperature)
    3. Polytropic (PV = C)
    4. Isometric (Constant Volume)
    5. Isentropic (Constant Entropy)
Work Types: Gravity, Electrical & Acceleration
  • Electrical work equation: W = ∫ F ds = mg dz.
    • Integrating: W = mg(h₂ - h₁)
  • The first law and gravitational energy interactions highlight changes in potential and kinetic energy during actions like dropping an object.
Nature of Energy Interactions (Heat)
  • Work vs. Heat:
    • Work is organized energy; Heat is disorganized energy transfer.
  • Modes of Heat Transfer include:
    1. Conduction
    2. Convection
    3. Radiation (photon/electromagnetic transfer)
  • Heat transfer requires close thermal contact.
Problem Analysis
  • Steps for analyzing a system:
    1. Draw schematic showing mass flow, heat, and work interactions.
    2. Define the system (closed or open).
    3. Identify phases involved in the system.
    4. Write conservation laws (mass, energy).
    5. Use equations of state or values from tables.
    6. Visualize the process on a diagram (P-v, T-v, etc.) and ensure solvability.
Example Problem
  • A container with 5m³ holds 0.05m³ liquid and the rest vapor at 0.1 MPa. Heating it until the liquid evaporates completely. Calculate required heat.
New Properties: Enthalpy
  • Enthalpy is defined in relation to internal energy, pressure, and volume:
    • H = U + PV (useful for defining total energy changes).
    • Heat relationship: ΔQ = H₂ - H₁.
New Properties: Specific Heats
  • Two forms of energy lead to the definition of specific heats at constant volume and constant pressure:
    • In incompressible substances, specific heats are consistent (Cp = Cv = C).
    • For fluids, relationships can be derived: ΔH = ΔU + vΔP.
Specific Heats and Ideal Gases
  • Specific heats of gases vary with pressure and temperature. An average constant value over small temperature ranges is used.
General Systems with Work
  • Mechanical work can be defined in terms of force, pressure, area, and the displacement of surfaces.
Mass Conservation
  • Mass is conserved except in relativistic conditions. Basic conservation: Internal property change + through-flow = Sum of sources.