🔥Thermodynamics I Unit 4 – Energy Analysis of Closed Systems

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, and energy in systems
• A system is a region in space or quantity of matter under study
• The surroundings include everything external to the system
• The system boundary separates the system from its surroundings
• A closed system allows energy transfer across its boundaries but no mass transfer
• An open system allows both mass and energy transfer across its boundaries
• State refers to the condition of a system, typically described by properties like temperature, pressure, and volume
• A process is a change in the state of a system from an initial state to a final state

Energy Forms and Transfer

• Energy is the capacity to do work or transfer heat
• Kinetic energy is associated with the motion of an object
• Potential energy is associated with the position or configuration of an object
• Internal energy is the sum of the microscopic kinetic and potential energies of a system
• Heat is the transfer of energy due to a temperature difference between a system and its surroundings
  • Occurs from high temperature to low temperature regions
  • Represented by the symbol $Q$
• Work is the transfer of energy due to a force acting through a distance
  • Occurs when a system interacts with its surroundings, causing a displacement
  • Represented by the symbol $W$

First Law of Thermodynamics

• The first law of thermodynamics is an expression of the conservation of energy principle
• It states that energy cannot be created or destroyed, only converted from one form to another
• For a closed system, the change in the system's energy equals the net energy transfer to the system
• Mathematically expressed as $\Delta E = Q - W$
  • $\Delta E$ is the change in the system's total energy
  • $Q$ is the net heat transfer to the system (positive if heat is added, negative if heat is removed)
  • $W$ is the net work done by the system (positive if work is done by the system, negative if work is done on the system)
• The first law provides a framework for analyzing energy changes in thermodynamic processes

Closed System Analysis

• In a closed system, no mass crosses the system boundary, but energy can be exchanged as heat or work
• The first law of thermodynamics is applied to analyze energy changes in closed systems
• The change in the system's energy is determined by the net heat transfer and net work done
• Examples of closed systems include:
  • A piston-cylinder device with a fixed mass of gas
  • A sealed, insulated container with a fixed quantity of liquid
• Analyzing closed systems involves identifying the system boundary, initial and final states, and energy interactions

Work in Thermodynamic Systems

• Work is an important mode of energy transfer in thermodynamic systems
• Mechanical work occurs when a force acts through a distance, such as a piston moving in a cylinder
• Electrical work involves the flow of electric current through a potential difference
• Shaft work is associated with the rotation of a shaft, such as in a turbine or compressor
• Boundary work (or $PV$ work) is the work done by a system due to changes in its volume against an external pressure
  • Calculated using $W = \int P dV$, where $P$ is the external pressure and $dV$ is the change in volume
• The sign convention for work is positive when done by the system and negative when done on the system

Internal Energy and Enthalpy

• Internal energy ($U$) is the sum of the microscopic kinetic and potential energies of a system
• It is a state function, meaning its change depends only on the initial and final states, not the path taken
• Enthalpy ($H$) is another thermodynamic property defined as $H = U + PV$
  • $U$ is the internal energy, $P$ is the pressure, and $V$ is the volume
• Enthalpy is useful when analyzing processes at constant pressure, such as in open systems
• Changes in internal energy and enthalpy are related to heat transfer and work in a process
• For a closed system, $\Delta U = Q - W$ and $\Delta H = Q_P$, where $Q_P$ is the heat transfer at constant pressure

Specific Heats and Energy Tables

• Specific heat is the amount of energy required to raise the temperature of a unit mass of a substance by one degree
• Specific heat at constant volume ($c_v$) is the specific heat when the volume is held constant
• Specific heat at constant pressure ($c_p$) is the specific heat when the pressure is held constant
• The specific heats are related by $c_p - c_v = R$, where $R$ is the specific gas constant
• Thermodynamic properties, including specific heats, are often tabulated in energy tables for various substances
  • Tables provide data at different temperatures and pressures
  • Interpolation or extrapolation may be necessary for values not directly listed
• Using specific heats and energy tables simplifies the calculation of energy changes in thermodynamic processes

Problem-Solving Strategies

• Identify the system and its boundaries, specifying whether it is open or closed
• Determine the initial and final states of the system
• Apply the first law of thermodynamics, considering heat transfer and work interactions
• Use appropriate sign conventions for heat and work (positive for heat added and work done by the system, negative for heat removed and work done on the system)
• Employ specific heat and energy table data when necessary to calculate energy changes
• Consider assumptions and simplifications, such as constant pressure or temperature processes
• Analyze the results and check for consistency with physical laws and principles
• Perform unit conversions and dimensional analysis to ensure proper units in the solution