4.2 Conservation of energy and the first law
2 min read•august 6, 2024
The is all about energy conservation. It's the foundation for understanding how energy moves and changes in systems. This law helps us track energy as it flows in and out, whether through heat, work, or mass transfer.
We use equations to apply the first law to real-world situations. These equations let us analyze both closed systems, which don't exchange mass, and open systems, which do. Understanding these concepts is key to solving thermodynamic problems.
First Law and Energy Balance
Conservation of Energy
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- First law of thermodynamics states energy cannot be created or destroyed, only converted from one form to another
- Energy balance is the accounting of energy transfer into and out of a system
- Based on the principle of
- Includes , work, and changes in internal, kinetic, and
- does not exchange mass with its surroundings, only energy (heat and work)
- Examples include a sealed piston-cylinder device or a rigid, sealed tank
- exchanges both mass and energy with its surroundings
- Also known as a
- Examples include a turbine, nozzle, diffuser, or heat exchanger
Energy Balance Equations
- First law for a closed system:
- is the change in total energy of the system (internal, kinetic, and potential)
- is the net heat transfer into the system
- is the net work done by the system
- Energy balance for an open system:
- is the change in total energy of the control volume
- is the mass flow rate
- is the , is the specific , and is the specific potential energy
Thermodynamic Processes
Steady-State and Transient Processes
- occurs when a system operates under steady conditions and all properties are independent of time
- Examples include a power plant operating at constant load or a refrigerator maintaining a constant temperature
- occurs when a system undergoes changes in its properties with time
- Also known as an unsteady process
- Examples include startup or shutdown of a power plant, or a batch chemical reactor
Adiabatic and Isothermal Processes
- occurs when there is no heat transfer between a system and its surroundings ()
- Can be reversible (quasi-equilibrium) or irreversible
- Examples include a well-insulated piston-cylinder device or a rapid expansion or compression
- occurs at constant temperature
- Requires heat transfer between the system and surroundings to maintain constant temperature
- Examples include a piston-cylinder device with a heat reservoir, or a phase change process at constant pressure (boiling or condensation)
Key Terms to Review (20)
Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings, meaning that any change in internal energy is solely due to work done on or by the system. This concept is crucial in understanding how different thermodynamic properties and state variables behave when energy transfer occurs without heat exchange.
Closed System: A closed system is a physical system that does not exchange matter with its surroundings but can exchange energy in the form of heat or work. This concept is crucial in understanding how energy conservation principles apply within a defined boundary, which influences various thermodynamic processes and behaviors.
Conservation of Energy: Conservation of energy is a fundamental principle stating that energy cannot be created or destroyed, only transformed from one form to another. This concept is essential in understanding how systems operate, as it applies to both closed systems, where no mass enters or leaves, and open systems, where mass and energy can exchange with the surroundings. Energy conservation emphasizes that the total energy within a system remains constant unless acted upon by external forces, highlighting the interconnectedness of various forms of energy in both mechanical and thermal processes.
Control Volume: A control volume is a defined region in space used in thermodynamics to analyze the behavior of fluid systems. It serves as a boundary that can be either fixed or movable, allowing for the exchange of mass, energy, and momentum with its surroundings. Understanding control volumes is crucial for applying principles like conservation of energy and analyzing systems, whether they are closed or open.
Energy Balance: Energy balance refers to the principle that the total energy entering a system must equal the total energy leaving that system, in accordance with the first law of thermodynamics. This concept highlights how energy is conserved within a defined boundary and can change forms, such as from kinetic to potential energy, but is never lost. It serves as a fundamental principle in analyzing how systems behave under different conditions and is crucial for understanding processes involving heat transfer, work, and internal energy changes.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This fundamental principle connects various concepts such as conservation of energy, the relationship between heat and work, and how energy transfers occur in both closed and open systems.
Heat Transfer: Heat transfer is the process of thermal energy moving from one body or system to another due to a temperature difference. This movement can occur through conduction, convection, or radiation, and it plays a crucial role in understanding energy conservation and the efficiency of thermal systems. Recognizing how heat transfer operates helps us analyze the directionality of processes and optimize thermal efficiency in various applications.
Internal Energy: Internal energy is the total energy contained within a thermodynamic system, encompassing both kinetic and potential energy at the molecular level. This concept is vital for understanding how energy is stored and transformed during processes such as heating, cooling, and phase changes, linking closely with heat transfer, work done on or by the system, and state variables that define the system's condition.
Isothermal process: An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout the entire process. This means that any heat added to the system is used to do work, and vice versa, maintaining equilibrium between heat transfer and work done.
James Prescott Joule: James Prescott Joule was a British physicist and brewer known for his contributions to the study of energy and thermodynamics, particularly for formulating the law of conservation of energy. His work laid the groundwork for understanding the relationship between heat and mechanical work, which is fundamental to the principles governing thermodynamic systems.
Julius von Mayer: Julius von Mayer was a German physicist and one of the key figures in the development of the first law of thermodynamics, which articulates the principle of conservation of energy. He proposed that energy is neither created nor destroyed, only transformed from one form to another, a fundamental concept that underpins much of modern physics and engineering. His insights laid the groundwork for understanding energy transfer in various systems, impacting fields ranging from mechanical engineering to chemistry.
Kinetic Energy: Kinetic energy is the energy that an object possesses due to its motion. It depends on the mass of the object and the square of its velocity, expressed mathematically as $$KE = \frac{1}{2} mv^2$$, where 'm' is mass and 'v' is velocity. This concept connects to the conservation of energy, as kinetic energy can be transformed into other forms of energy, such as potential energy, while maintaining the overall balance in a system.
Open System: An open system is a type of thermodynamic system that can exchange both energy and matter with its surroundings. This means that substances can flow in and out of the system, allowing for the transfer of heat, work, and mass. Open systems are crucial for understanding various natural and engineered processes, including energy conversions and chemical reactions.
Potential Energy: Potential energy is the stored energy in an object due to its position or configuration within a force field, such as gravitational or elastic forces. This energy can be converted into kinetic energy when the object's position changes, illustrating the fundamental concept of energy transformation. In relation to energy, heat, and work, potential energy plays a crucial role in understanding how systems can store energy and later release it to perform work.
Specific Enthalpy: Specific enthalpy is a thermodynamic property defined as the total heat content of a system per unit mass. It combines internal energy with the energy associated with pressure and volume, represented mathematically as $$h = u + pv$$, where $$h$$ is specific enthalpy, $$u$$ is internal energy, $$p$$ is pressure, and $$v$$ is specific volume. This property is crucial for analyzing energy transfers and transformations in fluid systems, particularly when dealing with processes that involve heat and work interactions.
Steady-State Process: A steady-state process refers to a condition in a system where all properties remain constant over time, despite ongoing processes that may be occurring within the system. In this state, the input and output flows are balanced, leading to no accumulation of mass or energy within the system. This concept is fundamental when discussing the conservation of energy and applying the first law of thermodynamics, as it simplifies calculations by allowing for assumptions about uniformity in conditions.
Transient Process: A transient process is a temporary state in which a system undergoes changes in its properties over time until it reaches a steady state. During this phase, various parameters, such as temperature, pressure, and energy content, are not constant and evolve until they stabilize. Understanding transient processes is crucial for analyzing how systems respond to external changes and for applying the conservation of energy principles effectively.
Work done on/by the system: Work done on/by the system refers to the energy transfer that occurs when a force is applied to a system, causing it to move or change its state. In thermodynamics, this concept is crucial because it connects mechanical energy to thermal energy, illustrating how energy can be transformed and conserved within a closed system. Understanding this concept allows for a clearer interpretation of how systems interact with their surroundings, particularly in terms of energy changes that occur during processes like expansion and compression.
δe_cv = q - w + ∑_in 𝑚̇(ℎ + v^2/2 + gz) - ∑_out 𝑚̇(ℎ + v^2/2 + gz): This equation represents the energy balance for a control volume, illustrating how the change in internal energy (δe_cv) is affected by heat transfer (q), work done (w), and the energy contributions from mass flow into and out of the system. It connects to fundamental principles by emphasizing how energy can neither be created nor destroyed, but only transformed or transferred, aligning with the first law of thermodynamics.
δe_system = q - w: The equation $$\delta e_{system} = q - w$$ represents the change in internal energy of a system, where $$q$$ is the heat added to the system and $$w$$ is the work done by the system. This fundamental relationship highlights how energy is conserved in thermodynamic processes, illustrating that any increase in a system's internal energy can be attributed to the heat added and the work done on or by the system. It emphasizes the balance between energy transfers and the importance of understanding how systems interact with their surroundings.