4.2 Energy balance for closed systems
4 min read•july 30, 2024
Energy balance for closed systems is a crucial concept in thermodynamics. It applies the first law to systems that don't exchange matter with their , focusing on energy transfers through heat and work.
Understanding this topic helps you analyze various processes in closed systems. You'll learn to use energy balance equations, relate thermodynamic properties, and solve problems involving different types of work and .
Thermodynamics of Closed Systems
First Law of Thermodynamics
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- States energy cannot be created or destroyed, only converted from one form to another
- For a closed system, the change in total energy (ΔE) equals net heat transfer into the system (Q) minus net work done by the system (W): ΔE = Q - W
- Total energy of a closed system consists of (U), kinetic energy (KE), and potential energy (PE): E = U + KE + PE
- In the absence of kinetic and potential energy changes, the first law simplifies to ΔU = Q - W for a closed system
Application to Closed Systems
- Closed systems do not exchange matter with their surroundings, only energy in the form of heat and work
- Energy balance for a closed system undergoing a process: ΔU = Q - W, where ΔU is the change in internal energy, Q is net heat transfer, and W is net work done
- Examples of closed systems include a sealed piston-cylinder device, a rigid tank with no inlets or outlets, and a pressure cooker
Energy Balance Equations for Closed Systems
Process-Specific Energy Balance Equations
- Isochoric (constant volume) process: W = 0, becomes ΔU = Q
- Isobaric (constant pressure) process: W = P(V₂ - V₁), energy balance equation becomes ΔU = Q - P(V₂ - V₁)
- Isothermal (constant temperature) process: ΔU = 0, energy balance equation becomes Q = W
- (no heat transfer, Q = 0): energy balance equation becomes ΔU = -W
Relating Thermodynamic Properties
- Ideal gas law (PV = nRT) relates pressure, volume, temperature, and amount of substance for an ideal gas
- Specific heat capacities (Cv and Cp) relate temperature changes to internal energy and heat transfer
- Cv is the molar at constant volume: ΔU = nCvΔT
- Cp is the molar specific heat capacity at constant pressure: ΔH = nCpΔT, where ΔH is the change in
Problem Solving in Closed Systems
Problem-Solving Approach
- Identify the system, the process, and relevant energy terms (heat, work, internal energy change)
- Apply the appropriate energy balance equation based on the process and given information
- Use thermodynamic relations (ideal gas law, specific heat capacities) to relate changes in properties
- Determine the type of work (boundary work, shaft work) and calculate using appropriate formulas
- Solve for the unknown quantity using the energy balance equation and given information
Types of Work in Closed Systems
- Boundary work (or PV work) occurs when the system expands or contracts against an external pressure: W = P(V₂ - V₁)
- Shaft work involves the transfer of energy through a rotating shaft, such as in a turbine or compressor
- Other types of work include electrical work, spring work, and gravitational work
Example Problems
- A closed system undergoes an isobaric process at 2 atm, expanding from 1 L to 3 L. If 500 J of heat is added to the system, determine the change in internal energy.
- An ideal gas in a piston-cylinder device undergoes an isothermal compression from 5 L to 2 L at 300 K. Calculate the heat transfer and work done during the process.
Internal Energy and Energy Balance Analysis
Internal Energy as a State Function
- Internal energy (U) is the sum of the kinetic and potential energies of the particles within a system
- Includes translational, rotational, vibrational, and intermolecular energies
- As a state function, internal energy depends only on the current state, not the path taken to reach that state
Relationship between Internal Energy and Temperature
- For an ideal gas, the change in internal energy is proportional to the change in temperature: ΔU = nCvΔT
- n is the number of moles
- Cv is the molar specific heat capacity at constant volume
- ΔT is the temperature change
- The specific heat capacity relates the amount of heat required to change the temperature of a substance
Role of Internal Energy in Energy Balance Analysis
- Changes in internal energy (ΔU) are caused by heat transfer (Q) and work done (W) on or by the system
- The relates these quantities: ΔU = Q - W
- In energy balance analysis, internal energy is a key component in determining the heat transfer and work interactions between a system and its surroundings during a process
Key Terms to Review (18)
Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is transferred into or out of the system. During this type of process, any change in the internal energy of the system is solely due to work done on or by the system, making it essential in understanding how systems behave under different conditions.
Calorie: A calorie is a unit of energy defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. This term plays a crucial role in understanding how energy transfers through heat, work, and mass, and is integral to the calculations involved in internal energy, enthalpy, and specific heats. Additionally, calories are fundamental in energy balance equations, especially for closed systems where energy cannot enter or leave, helping quantify how much energy is stored or lost.
Energy balance equation: The energy balance equation is a fundamental principle that states that the energy entering a system must equal the energy leaving the system plus any change in the energy stored within that system. This concept is crucial for analyzing various processes and systems, enabling the calculation of energy transformations, efficiencies, and performance metrics in engineering applications.
Energy conservation: Energy conservation is the principle stating that energy cannot be created or destroyed, only transformed from one form to another. This concept is vital in understanding how energy flows within closed systems and how energy interactions occur in both closed and open systems. By applying the idea of energy conservation, we can analyze processes that involve work and heat transfer, leading to a better grasp of system efficiency and sustainability.
Enthalpy: Enthalpy is a thermodynamic property defined as the sum of a system's internal energy and the product of its pressure and volume, represented by the equation $$H = U + PV$$. This concept is crucial for understanding energy transfer in processes involving heat and work, especially in closed systems, where enthalpy changes can indicate how much energy is absorbed or released during physical and chemical transformations.
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 capacity equation: The heat capacity equation defines the amount of heat energy required to change the temperature of a substance by a certain amount. It is represented mathematically as $$C = \frac{Q}{\Delta T}$$, where $$C$$ is the heat capacity, $$Q$$ is the heat added or removed, and $$\Delta T$$ is the change in temperature. Understanding this equation is crucial for analyzing energy transfer in closed systems, as it helps quantify how much energy must be supplied to or removed from a system to achieve a desired temperature change.
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.
Internal energy: Internal energy is the total energy contained within a system, resulting from the kinetic and potential energies of its molecules. It plays a crucial role in determining the thermodynamic state of the system, affecting properties like temperature and pressure, and is essential for understanding energy transfer processes.
Isothermal process: An isothermal process is a thermodynamic process in which the temperature of a system remains constant while the system undergoes a change in volume or pressure. This type of process is crucial for understanding how systems interact with their surroundings and how energy is exchanged in various thermodynamic cycles.
Joule: A joule is the SI unit of energy, defined as the amount of energy transferred when a force of one newton is applied over a distance of one meter. It connects to various forms of energy transfer, including heat, work, and mass, highlighting the ways energy can be converted or transformed in different processes.
Second Law of Thermodynamics: The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time, and it tends to increase, leading to the concept that energy transformations are not 100% efficient. This law establishes the directionality of processes, implying that certain processes are irreversible and energy has a quality that degrades over time, connecting tightly to concepts of heat transfer, work, and system analysis.
Specific Heat Capacity: Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). This property is crucial for understanding how substances absorb and release heat, which relates closely to their internal energy, enthalpy, and behavior in different thermodynamic processes.
Steady State: Steady state refers to a condition in which a system's properties remain constant over time, despite ongoing processes or interactions. In this state, the system is not in equilibrium, but rather it is maintaining a balance between input and output, allowing for the continuous flow of matter and energy without changing the overall state of the system. This concept is crucial in understanding how systems function under constant conditions and helps in analyzing energy changes and material flows within closed systems.
Surroundings: Surroundings refer to everything external to a system that can interact with it, impacting its behavior and energy exchanges. This term plays a vital role in understanding how systems operate within their environment, especially regarding energy transfer and the boundaries that define what is included in the system versus what is not. Recognizing the surroundings helps in analyzing how energy moves between the system and its surroundings, which is crucial for evaluating energy balances in various scenarios.
System boundary: A system boundary is an imaginary line that separates a defined system from its surroundings, helping to identify what is included in the analysis of energy and mass transfer. Understanding this boundary is crucial because it allows us to determine how energy enters and leaves the system, which is essential for conducting energy balances and analyzing processes that involve fluid flow and other interactions with the environment.
Thermal conductivity: Thermal conductivity is a material property that quantifies the ability of a substance to conduct heat. This property plays a crucial role in energy transfer within and between systems, affecting how heat flows from areas of high temperature to low temperature. Understanding thermal conductivity is essential when analyzing energy balances in closed systems, as it impacts how energy is conserved or lost during thermal interactions.
Work Transfer: Work transfer refers to the energy exchanged between a system and its surroundings due to a force acting through a distance. This concept is crucial in understanding how energy moves in various processes, including those involving heat and mass. Work transfer can occur in multiple forms, such as mechanical work or boundary work, and plays a vital role in energy transformations within systems.