First Law of Thermodynamics and the First Law

Overview of Thermodynamics

• Class Objective: Understanding the behavior of engineering systems through the laws of thermodynamics.

Laws of Thermodynamics

• Main Laws:
  • First Law of Thermodynamics: Energy is conserved.
  • Second Law of Thermodynamics: Not discussed in detail but referenced.
• Additional Concepts: Discussion may include a third law, but focus is on the first two.

First Law of Thermodynamics

• Definition:
  • Energy can neither be created nor destroyed; it can only be transferred or changed from one form to another.
  • Mathematical Representation:
    $\Delta E<em>{universe} = \Delta E</em>{system} + \Delta E_{surroundings} = 0$
  • This implies that whatever the system gains, the surroundings lose and vice versa.

Energy Transfer in Thermodynamic Systems

• Types of Energy Transfer:
  • Work (W): Energy transferred by mechanical means.
  • Positive when performed on the system; negative when performed by the system.
  • Heat (Q): Energy transferred due to temperature difference.
  • Positive when heat enters the system; negative when heat exits the system.

Intrinsic Energy of Systems

• Internal Energy (U):
  • Definition: The energy of the molecules constituting a substance, inclusive of several components.
  • Components of Internal Energy:
    • Microscopic kinetic energy
    • Rotational energy of atoms within a molecule
    • Vibrational energy of atoms within a molecule
    • Potential energy due to molecular interactions
• Relationship with Thermodynamic Properties:
  • Internal energy is an intrinsic property related to the fundamental properties of the system: pressure, specific volume, temperature, and composition.

Components of Energy in a System

• Total Energy Composition:
  • $\Delta U = \Delta U_{internal} + \Delta KE + \Delta PE$
  • Where KE is kinetic energy and PE is potential energy.
• Application to Chemical Engineering Systems:
  • For many practical systems, kinetic and potential energy can often be ignored, leading to the simplified form of the first law:
    $\Delta U = Q + W$

Differential Formulation of First Law

• Differential Form:
  • $dU = Q<em>{in} + W</em>{in}$
  • Heat and work may need to be treated as inexact differentials compared to exact differentials like internal energy.

Equilibrium States

• Definition of Equilibrium:
  • A state of balance where properties do not change over time.
• Conditions for Equilibrium:
  • Mechanical forces are balanced (no work transfer).
  • No thermal gradients present (no heat transfer).
  • All measurable properties are uniform throughout the system.

Zeroth Law of Thermodynamics

• Statement:
  • If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
• Implications:
  • Used to define temperature; if two bodies are in thermal equilibrium, they share the same temperature.

State Functions vs Path Functions

• State Functions:
  • Properties that depend only on the current state of the system.
  • Examples: pressure, volume, temperature, internal energy.
  • Changes are independent of the path taken between two states.
• Path Functions:
  • Properties that depend on the specific path taken to achieve a state.
  • Examples: heat, work.

Examples of State Function vs Path Function

1. Internal Energy (State Function):
   • The change in internal energy can be computed solely by initial and final states.
2. Heat and Work (Path Functions):
   • Require knowledge of the specific path taken to determine values.

Quiz Concepts

• State Function Example:
  • Scenario involving a fixed starting and ending point (state 1 to state 2) where only state functions can be calculated directly.
• Work and Heat Examples:
  • Calculating work and heat would require additional path information since they are path functions.

Reversible Processes

• Definition:
  • An idealized process where the system is in equilibrium at all points, meaning that it can be reversed with an infinitesimal change.
• Characteristics of Reversible Processes:
  • No dissipative losses.
  • Every change occurs in a quasi-static manner at equilibrium.
• Importance:
  • Simplifies calculations and serves as a benchmark for real processes.

Ideal Gas Law

• Equation:
  • $PV = nRT$
  • Valid under conditions of low pressure and high temperature.
• Special Cases:
  • If isothermal conditions exist (constant temperature), neat relationships for state changes can be established.

Example Problem: Reversible Expansion of Gas

• Problem Statement:
  • Gas expands in a piston-cylinder arrangement at constant temperature and pressure.
• Key Assumptions:
  • Closed system, ideal gas characteristics, reversible process.
• Calculation Steps:
  • Calculate work done using the relations from the ideal gas law and the reversible expansion equations.