2.1 Energy conservation and the First Law

Energy conservation is the cornerstone of thermodynamics. The First Law states that energy can't be created or destroyed, only converted. This principle helps us understand how energy changes in various systems and processes.

The First Law equation, ΔE = Q - W, links heat, work, and energy changes. It applies to different forms of energy like kinetic, potential, and internal energy. Understanding this law is crucial for analyzing real-world systems like engines and refrigerators.

Energy Conservation and the First Law

First Law of Thermodynamics

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• States energy cannot be created or destroyed, only converted from one form to another (law of conservation of energy)
• Fundamental principle of energy conservation establishes relationship between heat, work, and energy in a thermodynamic system
• Change in a system's total energy ($\Delta E$) equals heat added to the system ($Q$) minus work done by the system ($W$)
  • Mathematically expressed as: $\Delta E = Q - W$
• Provides framework for analyzing energy changes in various processes (heat engines, refrigerators)

Forms of energy in systems

• Kinetic energy (KE): energy associated with motion of an object (moving car, flowing river)
  • $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity
• Potential energy (PE): energy associated with position or configuration of an object
  • Gravitational PE: $PE_g = mgh$, where $h$ is height (ball on a shelf, water in a reservoir)
  • Elastic PE: $PE_e = \frac{1}{2}kx^2$, where $k$ is spring constant and $x$ is displacement (compressed spring, stretched rubber band)
• Internal energy (U): sum of microscopic kinetic and potential energies of a system's particles
  • Depends on temperature, pressure, and volume (ideal gas, real fluids)
• Chemical energy: energy stored in chemical bonds (gasoline, batteries)
• Electrical energy: energy associated with electric charges and electric fields (power lines, capacitors)
• Thermal energy: energy associated with random motion of particles in a substance (hot coffee, molten lava)
• Energy can be converted from one form to another during thermodynamic processes (heat engine converts thermal energy to mechanical work)

First Law in thermodynamic processes

• Closed systems: no mass transfer across system boundaries
  • $\Delta E = Q - W$
  • $\Delta E = \Delta U$ (change in internal energy)
• Open systems: mass transfer across system boundaries
  • $\Delta E = Q - W + \Delta E_{mass}$, where $\Delta E_{mass}$ is change in energy due to mass transfer
• Isothermal process: constant temperature
  • Ideal gas: $W = nRT\ln\frac{V_2}{V_1}$, where $n$ is number of moles, $R$ is gas constant, and $V$ is volume
• Adiabatic process: no heat transfer ($Q = 0$)
  • $\Delta U = -W$
  • Ideal gas: $PV^\gamma = \text{constant}$, where $\gamma$ is specific heat ratio (compression in diesel engines, expansion in gas turbines)
• Isobaric process: constant pressure
  • $\Delta H = Q$, where $H$ is enthalpy (heating water in open container, melting of ice)
• Isochoric (isovolumetric) process: constant volume
  • $\Delta U = Q$ (heating gas in closed container, cooling of solid object)

Problem-solving with First Law

1. Identify system and its boundaries (control volume, surroundings)
2. Determine type of thermodynamic process (isothermal, adiabatic, isobaric, isochoric)
3. Apply appropriate form of First Law equation based on process and system
   • Closed system: $\Delta U = Q - W$
   • Open system: $\Delta E = Q - W + \Delta E_{mass}$
4. Calculate work done by considering process and system
   • Example: work done by ideal gas in isothermal expansion: $W = nRT\ln\frac{V_2}{V_1}$
5. Calculate heat transfer by considering process and system
   • Example: heat added in isobaric process: $Q = \Delta H$
6. Solve for unknown variable (work, heat, or change in energy) using First Law equation
7. Interpret results in context of energy conservation and specific thermodynamic process