3.3 First Law of Thermodynamics

The First Law of Thermodynamics is the cornerstone of energy conservation in physical systems. It states that energy can't be created or destroyed, only converted between forms. This principle is crucial for understanding how energy flows in various processes.

Applying the First Law helps us analyze different thermodynamic processes like isothermal, adiabatic, and isobaric changes. By understanding these processes, we can predict how systems behave and calculate important quantities like work, heat, and internal energy changes.

First Law of Thermodynamics

Application of first law of thermodynamics

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• Fundamental principle states energy cannot be created or destroyed, only converted from one form to another (law of conservation of energy)
• For a closed system, change in internal energy ($\Delta U$) equals heat added to the system ($Q$) minus work done by the system ($W$)
  • Mathematical representation: $\Delta U = Q - W$
• Heat ($Q$) is positive when added to the system (heating) and negative when removed from the system (cooling)
• Work ($W$) is positive when done by the system (expansion) and negative when done on the system (compression)
• Calculate changes in internal energy by:
  1. Determining heat added to or removed from the system (calorimetry)
  2. Calculating work done by or on the system (pressure-volume diagrams)
  3. Using the first law of thermodynamics equation to find $\Delta U$

Relationships in thermodynamic processes

• Isothermal process: temperature remains constant
  • Change in internal energy is zero ($\Delta U = 0$)
  • Heat added equals work done by the system ($Q = W$)
    • Example: isothermal expansion of an ideal gas
• Adiabatic process: no heat exchanged with surroundings
  • Change in internal energy equals negative of work done ($\Delta U = -W$)
    • Example: rapid compression of a gas in an insulated cylinder
• Isobaric process: pressure remains constant
  • Heat added equals change in internal energy plus work done by the system ($Q = \Delta U + W$)
    • Example: heating a gas at constant pressure
• Isochoric (isovolumetric) process: volume remains constant
  • No work is done ($W = 0$)
  • Heat added equals change in internal energy ($Q = \Delta U$)
    • Example: heating a gas in a rigid container
• Quasistatic process: system remains infinitesimally close to equilibrium throughout the entire process

State functions vs path-dependent quantities

• State functions depend only on the current state, not the path taken to reach that state
  • Examples: internal energy ($U$), enthalpy ($H$), entropy ($S$)
  • Changes in state functions ($\Delta U$, $\Delta H$, $\Delta S$) are independent of the path between initial and final states
    • Example: change in internal energy is the same for isothermal and adiabatic processes between the same initial and final states
• Path-dependent quantities depend on the specific path taken between initial and final states
  • Examples: heat ($Q$) and work ($W$)
  • Values of heat and work vary depending on the process or path, even if initial and final states are the same
    • Example: work done in an isothermal expansion differs from work done in an adiabatic expansion between the same initial and final volumes
• Identify state functions and path-dependent quantities to apply appropriate equations and principles when analyzing thermodynamic processes

Types of Thermodynamic Processes

• Reversible process: can be reversed without leaving any change in the system or surroundings
• Irreversible process: cannot be reversed without leaving a change in the system or surroundings
• Cyclic process: system returns to its initial state after a series of changes
• Thermodynamic equilibrium: system is in thermal, mechanical, and chemical equilibrium with its surroundings