3.3 Conservation of energy principle
4 min read•july 30, 2024
The principle is a cornerstone of thermodynamics. It states that energy can't be created or destroyed, only converted or transferred. This principle forms the basis of the , which quantifies energy changes in systems.
In thermodynamics, we apply this principle to closed and open systems. For closed systems, energy changes are due to heat and work. Open systems also consider mass flow. Understanding these concepts is crucial for analyzing real-world thermal processes.
Conservation of Energy in Thermodynamics
Fundamental Principle and First Law of Thermodynamics
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- The conservation of energy principle states that energy cannot be created or destroyed, only converted from one form to another or transferred between systems
- In a , the total energy remains constant, and any change in the system's energy is due to energy transfer across the system boundary in the form of heat or work
- The first law of thermodynamics is a statement of the conservation of energy principle, expressing that the change in a system's internal energy is equal to the heat added to the system minus the by the system
- The conservation of energy principle applies to all forms of energy, including thermal, mechanical, electrical, chemical, and nuclear energy (nuclear fission, nuclear fusion)
Energy Classification and Examples
- Energy can be classified as either stored (potential) or in transit (kinetic)
- Examples of stored energy include chemical (fossil fuels, batteries), nuclear (uranium), and gravitational (water in a reservoir)
- Examples of energy in transit include thermal (), mechanical (rotating shaft), and electrical energy (current in a circuit)
Energy Balance for Systems
Closed Systems
- In a closed system, no mass crosses the system boundaries, and the change in the system's energy is solely due to heat and work interactions with the surroundings
- For a closed system undergoing a process, the change in the system's total energy (ΔE) is equal to the heat added to the system (Q) minus the work done by the system (W):
- For a closed system, the change in total energy (ΔE) is equal to the change in the system's internal energy (ΔU), as there is no change in the system's kinetic or potential energy: ΔE = [ΔU = Q - W](https://www.fiveableKeyTerm:δu_=_q_-_w)
Open Systems
- In an open system, mass, as well as energy, can cross the system boundaries (steam turbine, heat exchanger)
- The conservation of energy principle must account for the energy associated with the mass flow in addition to heat and work interactions
- For an open system, the change in the system's total energy (ΔE) is equal to the heat added to the system (Q), minus the work done by the system (W), plus the energy associated with the mass entering the system (Emass,in), minus the energy associated with the mass leaving the system (Emass,out):
- The energy associated with the mass flow includes the enthalpy, , and potential energy of the flowing matter (steam, air, refrigerant)
Applying Conservation of Energy
Energy Balance Equations for Various Processes
- The general energy balance equation for a closed system undergoing a process is: , where ΔE is the change in the system's total energy, Q is the heat added to the system, and W is the work done by the system
- The energy balance equation for an open system, considering the steady-state flow process, is: , where Qnet is the net heat transfer rate, Wnet is the net work rate, ṁ is the mass flow rate, h is the specific enthalpy, ve is the velocity, g is the acceleration due to gravity, and ze is the elevation at the inlet (in) and outlet (out) of the system
- For a control volume with multiple inlets and outlets, the energy balance equation must account for the energy associated with each mass flow stream (power plant with multiple steam extractions)
Transient and Steady-State Processes
- In a transient (unsteady) process, the energy storage term must be included in the energy balance equation to account for the change in the system's energy over time (charging a compressed air storage tank)
- For steady-state processes, the energy storage term is zero, simplifying the energy balance equation (continuous operation of a gas turbine)
Energy Balance in Processes
Problem-Solving Approach
- Identify the system boundaries and determine whether the system is closed or open
- Determine the relevant energy interactions (heat, work, and mass flow) crossing the system boundaries
- Write the appropriate energy balance equation based on the type of system (closed or open) and the nature of the process (steady-state or transient)
- Identify the known and unknown variables in the energy balance equation
- Use the properties of the system (specific heats, enthalpies, pressures, and temperatures) to relate the unknown variables to the known variables
Interpreting Results and Checking Solutions
- Solve the energy balance equation for the desired unknown variable, such as the final temperature, heat transfer, work done, or mass flow rate
- Interpret the results and check the solution for consistency with the problem statement and physical laws
- Verify that the units of the solution are correct and consistent with the problem
- Check if the magnitude and sign of the solution make physical sense (positive heat transfer into the system, negative work done by the system)
- Confirm that the solution satisfies the conservation of energy principle and the first law of thermodynamics
Key Terms to Review (16)
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 and work. This concept is vital in understanding how energy flows and transforms within a defined environment without any mass transfer, influencing various thermodynamic processes and principles.
Coefficient of performance: The coefficient of performance (COP) is a measure of the efficiency of a heat pump, refrigerator, or air conditioning system, defined as the ratio of useful heating or cooling provided to the work input required to operate the system. It connects directly to how well energy is conserved and utilized in these systems, reflecting both the first law of thermodynamics and the second law efficiency in energy analysis.
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 principle underlies many physical processes and systems, ensuring that the total energy remains constant in an isolated system. Understanding this concept is crucial when analyzing how energy is converted during various processes, such as in thermodynamics and mechanical systems.
Efficiency: Efficiency is a measure of how well an energy conversion process uses the input energy to produce useful output energy, often expressed as a percentage. It reflects how much of the input energy is converted into useful work or output, with the remaining energy usually lost as waste heat. Understanding efficiency helps in evaluating the performance of various systems and devices, and plays a crucial role in improving energy utilization in both mechanical and thermal processes.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another, which means the total energy of an isolated system remains constant. This principle underlies various processes, cycles, and energy interactions that involve heat, work, and mass transfer in different systems.
Heat Engines: Heat engines are devices that convert thermal energy into mechanical work by taking in heat from a high-temperature source, performing work, and then releasing waste heat to a low-temperature sink. They operate on thermodynamic cycles and are essential for understanding how energy is transformed and utilized in various systems.
Heat Transfer: Heat transfer is the process of energy moving from a warmer object to a cooler one due to a temperature difference. This phenomenon plays a crucial role in various thermodynamic processes, affecting how systems interact with their surroundings and how energy is conserved or transformed within them.
Isolated System: An isolated system is a physical system that does not exchange matter or energy with its surroundings. This means that the total mass and energy within the system remains constant over time, making it a perfect model for studying thermodynamic principles. Understanding isolated systems is crucial for analyzing how energy transfers occur and the fundamental concepts surrounding thermodynamics, as they provide a clear framework to apply the conservation of energy principle without external influences.
Kinetic Energy: Kinetic energy is the energy that an object possesses due to its motion, defined mathematically as $$KE = \frac{1}{2}mv^2$$, where 'm' is the mass of the object and 'v' is its velocity. This concept is crucial in understanding how energy is conserved during physical processes and is a key factor in analyzing systems where fluid or mechanical motion occurs. Recognizing the relationship between kinetic energy and the work-energy principle helps explain how energy is transformed and transferred in various systems.
Mechanical Work: Mechanical work refers to the energy transferred to or from an object via the application of force along a displacement. This concept is crucial in understanding how energy changes form and is conserved in physical systems, highlighting the relationship between force, motion, and energy. In thermodynamics, mechanical work plays a pivotal role in processes where systems interact with their environment, such as in engines or when compressing gases.
Potential Energy: Potential energy is the energy stored in an object due to its position or configuration. It is a form of energy that can be converted into kinetic energy when an object moves or changes its state, playing a crucial role in understanding how energy is conserved and transformed in various systems. This concept is foundational for analyzing how energy behaves in both mechanical systems and fluid flows.
Q = mcδt: The equation $$q = mc\Delta T$$ represents the heat transfer (q) in a substance, where m is the mass, c is the specific heat capacity, and $$\Delta T$$ is the change in temperature. This equation illustrates how energy is conserved during thermal processes, showing that the amount of heat absorbed or released by a material is directly proportional to its mass and the change in temperature it undergoes. Understanding this relationship is essential for analyzing how systems interact with their surroundings when energy is exchanged.
Refrigerators: Refrigerators are devices that remove heat from a designated area and transfer it to another, typically to keep food and beverages cool. They operate based on thermodynamic principles, utilizing a refrigerant to absorb and expel heat through a cycle of evaporation and condensation, making them essential for food preservation and climate control.
Thermal Energy: Thermal energy is the internal energy present in a system due to the random motions of its particles. This energy is a key concept in understanding how heat transfers between systems and how energy conservation plays a role in physical processes. The behavior of thermal energy is fundamental to the laws of thermodynamics, particularly in analyzing how systems respond to heat exchanges and the energy stored within various states of matter.
Work Done: Work done is the energy transferred to or from an object via the application of force along a displacement. It plays a crucial role in understanding how systems interact with their surroundings, as it relates to energy changes within these systems. By analyzing work done, one can better grasp the principles of energy conservation and how different forms of work, especially in moving boundaries, affect a system's state during reversible and irreversible processes.
δu = q - w: The equation $$\delta u = q - w$$ represents the first law of thermodynamics, indicating that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This relationship highlights how energy transfers occur within a closed system, linking concepts like heat transfer, work, and internal energy. Understanding this equation is crucial as it lays the groundwork for various thermodynamic analyses and helps in understanding energy conservation principles in both physical and chemical processes.