Thermodynamics Basics and Laws

Thermodynamics

• Definition: The branch of physics that deals with heat, work, temperature, and energy.

• Laws of Thermodynamics:

  1. Zeroth Law:
     • If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
  2. First Law (Law of Energy Conservation):
     • Energy cannot be created or destroyed, only transformed.
     • Mathematical Form: ΔU = Q - W
       • ΔU: Change in internal energy
       • Q: Heat added to the system
       • W: Work done by the system
  3. Second Law:
     • In any energy transfer, the total entropy of an isolated system can only increase over time.
     • Energy transformations are not 100% efficient; some energy becomes unavailable for work.
  4. Third Law:
     • As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.

• Key Concepts:

  • Heat: Form of energy transfer due to temperature difference.
  • Work: Energy transfer resulting from a force acting over a distance.
  • Internal Energy: Total energy contained within a system.
  • Entropy: Measure of disorder or randomness in a system.

• Thermodynamic Processes:

  • Isothermal: Constant temperature (Q = W).
  • Adiabatic: No heat exchange (Q = 0).
  • Isobaric: Constant pressure (ΔU = Q - PΔV).
  • Isochoric: Constant volume (W = 0).

• Carnot Theorem:

  • No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

• Applications:

  • Heat engines: Devices converting heat to work (e.g., car engines).
  • Refrigerators and heat pumps: Devices transferring heat from cold to hot reservoirs.

• Thermodynamic Systems:

  1. Open System: Can exchange energy and matter with its surroundings.
  2. Closed System: Can exchange energy but not matter with its surroundings.
  3. Isolated System: Cannot exchange energy or matter with its surroundings.

• Equations of State:

  • Describe the state of a material (e.g., Ideal Gas Law: PV = nRT).

• Specific Heat: Amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius.

• Phase Changes:

  • Heat can cause changes in the state of matter (e.g., melting, boiling) without changing temperature.

Center of Mass

• What is it? It's a point that represents the average position of a body's mass distribution.
• How is it calculated? You can calculate it for a system of particles using a simple formula that sums the product of each particle's mass and its coordinates, divided by the total mass. For continuous mass distributions, integrals are used instead.
• Important properties: The COM acts as a single point where all the external forces are applied. It's also the same as the center of gravity in a uniform gravitational field.
• Motion: The COM's motion is determined by the net external force acting on the system. It follows Newton's second law and will remain at rest or at constant velocity if no external forces are present.
• Applications: It's widely used in understanding collisions, explosions, and motion in biomechanics, robotics, and multi-body dynamics.
• Types of COMs: The location of the COM is influenced by the object's symmetry and mass distribution. Even asymmetric objects have a COM, which could lie outside the object's physical structure.
• Examples: A uniform rod's COM is at its geometric center. A hollow sphere's COM is also at its geometric center due to its symmetry.
• Real-world considerations: The COM might not always reside within the object itself—consider a doughnut, where the COM is in the center of the hole.