Energy analysis of systems is crucial in understanding how energy flows and transforms within thermodynamic processes. This topic dives into the application of the First Law of Thermodynamics, exploring energy balances for closed and open systems.

We'll examine work and heat interactions, key components in energy transfer. We'll also explore energy efficiency concepts, including thermal efficiency, Carnot efficiency, and coefficient of performance, which are essential for evaluating system performance.

Thermodynamic Systems and Boundaries

Defining Thermodynamic Systems

• Thermodynamic systems are defined as a region in space or a quantity of matter bounded by a closed surface
• The surroundings encompass everything external to the system boundary
• The system boundary separates the system from its surroundings, allowing for the exchange of energy and/or mass depending on the type of system

Types of Thermodynamic Systems

• Closed systems have fixed amounts of mass with no mass transfer across the system boundary (a sealed piston-cylinder device)
• Open systems allow for mass transfer across the boundary (a steam turbine with inlet and outlet flows)
• Isolated systems do not interact with the surroundings, with no exchange of energy or mass across the boundary (a perfectly insulated container)
• Adiabatic systems do not allow heat transfer across the boundary (a well-insulated thermos)
• Diathermal systems permit heat transfer across the boundary (a heat exchanger)

Energy Analysis of Systems

First Law of Thermodynamics

• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
• The law provides a framework for analyzing energy conservation in thermodynamic systems
• It takes into account the various forms of energy, such as internal energy, kinetic energy, and potential energy

Energy Balance for Closed Systems

• For a closed system, the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W): $ΔU = Q - W$
• Internal energy is a state function that depends on the system's properties, such as temperature and pressure
• Heat and work are path functions, meaning their values depend on the process path taken by the system

Energy Balance for Open Systems

• For an open system, the energy balance equation includes the terms for the energy entering and leaving the system with the mass flow: $ΔE_system = Q - W + Σ(m_in * h_in) - Σ(m_out * h_out)$, where h is the specific enthalpy
• The steady-state assumption for open systems implies that the system's properties do not change over time, simplifying the energy balance equation
• Examples of open systems include gas turbines, compressors, and heat exchangers

Work and Heat Interactions

Work in Thermodynamic Systems

• Work is the energy transfer associated with a force acting through a distance, expressed as $W = ∫F ds$
• In thermodynamic systems, common forms of work include:
  • Boundary work: work done by the system due to expansion or compression (a piston-cylinder device)
  • Shaft work: work done by a rotating shaft (a turbine or compressor)
  • Electrical work: work done by an electrical device (a motor or generator)

Heat Transfer Mechanisms

• Heat is the energy transfer due to a temperature difference between the system and its surroundings, expressed as $Q = ∫T dS$, where T is the absolute temperature and S is the entropy
• Heat transfer can occur through three main mechanisms:
  • Conduction: heat transfer through direct contact between substances (a metal rod heated at one end)
  • Convection: heat transfer by fluid motion (a hot air balloon rising due to buoyancy)
  • Radiation: heat transfer through electromagnetic waves (the Earth receiving energy from the Sun)

Energy Efficiency of Systems

Thermal Efficiency

• Thermal efficiency is the ratio of the useful work output to the total heat input in a thermodynamic cycle or process: $η_th = W_net / Q_in$
• It measures the effectiveness of a system in converting heat input into useful work output
• Examples of systems where thermal efficiency is important include heat engines (internal combustion engines, steam turbines) and power plants

Carnot Efficiency

• The Carnot efficiency is the maximum theoretical efficiency for a heat engine operating between two thermal reservoirs at temperatures T_H (hot) and T_C (cold): $η_Carnot = 1 - (T_C / T_H)$
• It represents the upper limit for the efficiency of any heat engine operating between the same temperature reservoirs
• The Carnot cycle consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression

Coefficient of Performance

• The coefficient of performance (COP) is used to evaluate the efficiency of refrigeration and heat pump systems
  • For refrigerators: $COP_ref = Q_L / W_net$, where Q_L is the heat removed from the low-temperature reservoir
  • For heat pumps: $COP_hp = Q_H / W_net$, where Q_H is the heat delivered to the high-temperature reservoir
• The COP represents the ratio of the desired energy transfer (cooling or heating) to the work input required

Exergy Analysis

• Exergy analysis assesses the maximum useful work that can be obtained from a system in a given state and environment
• It helps identify inefficiencies and potential improvements in thermodynamic systems by considering both the quantity and quality of energy
• Exergy is the portion of energy that can be converted into useful work, while anergy is the portion that cannot be used for work (waste heat)