15.2 The First Law of Thermodynamics and Some Simple Processes
3 min read•june 18, 2024
Heat engines are the workhorses of thermodynamics, converting thermal energy into mechanical work. They absorb heat from a hot source, do work, and expel remaining heat to a cooler sink. Their efficiency is always less than 100%.
Thermodynamic processes are the building blocks of heat engines. These include isobaric (constant pressure), (constant volume), (constant temperature), and (no heat exchange) processes. Understanding these helps us analyze real-world systems.
The First Law of Thermodynamics
Operation of heat engines
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- Converts thermal energy into mechanical work through a
- Absorbs heat from a high-temperature reservoir (heat source) (e.g., a hot gas or steam)
- Converts some of the absorbed heat into useful work (e.g., moving a piston or turning a turbine)
- Expels the remaining heat to a low-temperature reservoir (heat sink) (e.g., the atmosphere or a cooling system)
- Efficiency defined as the ratio of work output to heat input
- Always less than 100% due to the Second Law of Thermodynamics which limits the maximum efficiency of heat engines (Carnot efficiency)
- Real-world examples include internal combustion engines (cars) and steam turbines (power plants)
Thermodynamic Systems and State Functions
- A is a defined region of matter under study
- State functions are properties that depend only on the current state of the system, not its history
- Examples include temperature, pressure, and volume
- The relates state variables for a given substance
- For an ideal gas, PV = nRT is the equation of state
- is the amount of heat required to raise the temperature of a substance by one degree
Simple Thermodynamic Processes
Types of thermodynamic processes
- occurs at constant pressure
- Work done calculated as
- Examples include a piston moving in a cylinder with constant external pressure or a gas expanding in a balloon
- Isochoric (isovolumetric) process occurs at constant volume
- No work is done
- Examples include heating a gas in a rigid container or a chemical reaction in a sealed vessel
- occurs at constant temperature
- For an ideal gas
- Work done calculated as
- Examples include slow compression or expansion of a gas allowing heat exchange with the surroundings
- involves no heat exchange with the surroundings
- For an ideal gas , where
- Work done calculated as
- Examples include rapid compression or expansion of a gas (sound waves) or adiabatic flame temperature in combustion
- Processes can be classified as reversible or irreversible
- A can be reversed without leaving any trace on the surroundings
- An cannot be reversed without changing the surroundings
Work in cyclical processes
- System returns to its initial state in a cyclical process
- Net change in is zero
- for a cyclical process
- Net heat absorbed equals the net work done
- Direction of heat and work determine sign convention (heat absorbed and work done by the system are positive)
- Calculate work done by finding the area enclosed by the process curve on a diagram
- For a simple rectangular process
- For more complex processes, integrate the pressure with respect to volume
- Examples include the (gasoline engines), (diesel engines), and (steam power plants)
Key Terms to Review (37)
Adiabatic: An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings. The system's temperature can change, but all energy transfer occurs as work.
Adiabatic Process: An adiabatic process is a thermodynamic process in which a system exchanges no thermal energy with its surroundings. This means that the system neither gains nor loses heat during the process, and all changes in the system's energy are due to work done on or by the system.
Angular momentum quantum number: The angular momentum quantum number, denoted by $l$, determines the shape of an electron's orbital and its orbital angular momentum. It can take any integer value from 0 to $n-1$, where $n$ is the principal quantum number.
Closed System: A closed system is a thermodynamic system that does not exchange matter with its surroundings, but may exchange energy. It is isolated from the transfer of matter but can interact with its environment through the transfer of energy, such as heat or work.
Cyclical Process: A cyclical process is a series of events that repeat in a predictable pattern, often leading to a return to the initial state after completing one full cycle. In thermodynamics, this concept is essential as it describes how systems can undergo various transformations while conserving energy, with changes in pressure, volume, and temperature that ultimately restore the system to its original conditions. Understanding cyclical processes allows for a deeper grasp of energy exchanges and the efficiency of engines and refrigerators.
Diesel Cycle: The diesel cycle is a thermodynamic cycle that describes the operation of a diesel engine. It is a type of internal combustion engine that uses the heat of compression to ignite the fuel, rather than using an electric spark as in a gasoline engine.
Enthalpy: Enthalpy is a measure of the total energy of a thermodynamic system, including its internal energy and the work done by or on the system as a result of changes in pressure and volume. It represents the sum of a system's internal energy and the work done on the system by its surroundings or the work done by the system on its surroundings.
Equation of State: The equation of state is a fundamental relationship in thermodynamics that describes the state of a substance, typically a gas or a fluid, in terms of its pressure, volume, and temperature. It provides a mathematical expression that allows the calculation of one of these properties given the other two, and it is crucial in understanding the behavior of systems undergoing thermodynamic processes.
First Law of Thermodynamics: The first law of thermodynamics states that energy can be converted from one form to another, but it cannot be created or destroyed. It is a fundamental principle that describes the relationship between energy, work, and heat in a system.
Heat Capacity: Heat capacity is a measure of the amount of energy required to raise the temperature of a substance by a certain amount. It quantifies how much heat a material can absorb or release without undergoing a significant change in temperature. This concept is crucial in understanding the thermal properties of materials and their behavior during various thermodynamic processes.
Heat engine: A heat engine is a device that converts thermal energy into mechanical work by exploiting the temperature difference between a hot and a cold reservoir. It operates in cycles, absorbing heat from the hot reservoir and expelling some of it to the cold reservoir while performing work.
Internal energy: Internal energy is the total energy contained within a thermodynamic system, arising from the kinetic and potential energies of its molecules. It is a state function and depends only on the current state of the system.
Internal Energy: Internal energy is the total kinetic and potential energy of all the atoms and molecules within a thermodynamic system. It represents the total energy contained within a system, excluding any external energy sources or work done on the system. This term is central to understanding various topics in thermodynamics, including the relationship between heat, temperature, and energy transformations.
Irreversible process: An irreversible process is a thermodynamic process that cannot return both the system and the surroundings to their original states. Irreversibility often results from factors like friction, unrestrained expansion, or heat transfer through a finite temperature difference.
Isobaric process: An isobaric process is a thermodynamic process in which the pressure remains constant. Heat added or removed from the system does work on or by the system while changing its internal energy.
Isobaric Process: An isobaric process is a thermodynamic process in which the pressure of a system remains constant throughout the process. This means that the system experiences no change in pressure, even as other variables like volume, temperature, or internal energy may change.
Isochoric: An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume does not change, no work is done by the system during this process.
Isochoric Process: An isochoric process, also known as an isovolumetric process, is a thermodynamic process in which the volume of a system remains constant while other properties, such as temperature and pressure, may change. This type of process is an important concept in the study of the First Law of Thermodynamics and the behavior of simple systems.
Isothermal: An isothermal process is a thermodynamic process in which the temperature of the system remains constant. Heat transfer occurs to maintain this constant temperature.
Isothermal Process: An isothermal process is a thermodynamic process in which the temperature of a system remains constant. This means that the system exchanges heat with its surroundings in such a way that the temperature of the system does not change throughout the process.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It measures the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
Joule: The joule (J) is the standard unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter. The joule is a fundamental unit that connects various topics in physics, from work and energy to thermodynamics and electricity.
Open System: An open system is a physical system that can exchange both energy and matter with its surroundings. This concept is crucial for understanding how systems interact with their environment and influence the behavior of various thermodynamic processes. Open systems are essential in many real-world applications, where the flow of energy and matter impacts everything from biological processes to industrial operations.
Otto cycle: The Otto cycle is a thermodynamic cycle that describes the functioning of a typical spark ignition piston engine, commonly found in automobiles. It consists of two isochoric (constant volume) and two adiabatic (no heat transfer) processes.
Otto Cycle: The Otto cycle is a thermodynamic cycle that describes the operation of a four-stroke internal combustion engine. It is named after Nikolaus Otto, who invented the four-stroke engine in 1876. The Otto cycle is closely related to the concepts of the First Law of Thermodynamics and the Second Law of Thermodynamics, as it involves the conversion of heat energy into mechanical work.
PV Diagram: A PV diagram, also known as a pressure-volume diagram, is a graphical representation of the relationship between the pressure and volume of a system, typically used in the context of thermodynamics. It provides a visual tool to analyze the behavior of a system undergoing various thermodynamic processes.
Q: Q is a symbol used to represent various physical quantities in different contexts, such as flow rate, heat, and electric charge. It is a versatile term that connects important concepts across multiple areas of physics, including fluid dynamics, thermodynamics, and electromagnetism.
Rankine Cycle: The Rankine cycle is a thermodynamic cycle that describes the operation of steam-powered turbine power plants. It is named after the Scottish engineer William John Macquorn Rankine, who was a pioneer in the field of thermodynamics and proposed this model for the efficient conversion of heat into work.
Reversible Process: A reversible process is a thermodynamic process that can be reversed without leaving any trace on the surroundings. In a reversible process, the system and the surroundings can be restored to their initial states without the expenditure of any work or the absorption of any heat from external sources.
Specific Heat Capacity: Specific heat capacity is a physical property that describes the amount of heat required to raise the temperature of a unit mass of a substance by one degree. It is a measure of a material's ability to store thermal energy and is an important concept in understanding heat transfer and temperature changes.
State Function: A state function is a property of a thermodynamic system that depends only on the current state of the system, and not on the path taken to reach that state. It is a variable that can be used to fully describe the condition of a system at a given point in time, without needing to know the history of how the system arrived at that state.
Thermodynamic System: A thermodynamic system refers to a defined region in space that is the focus of a thermodynamic analysis. It is a collection of matter and energy that can exchange heat and work with its surroundings, allowing the study of energy transformations and the application of thermodynamic principles.
W: In the context of thermodynamics, W represents work, which is the energy transferred by a force acting over a distance. Work is essential to understanding how energy is exchanged within a system, particularly in processes involving heat transfer and mechanical energy. It plays a crucial role in various thermodynamic processes, helping to explain how energy moves and transforms in physical systems.
ΔP: ΔP, or the change in pressure, refers to the difference between two pressure values, typically experienced within a fluid system. This concept is crucial in understanding gauge pressure and absolute pressure measurements, as well as how pressure affects energy transfer in thermodynamic processes. By calculating ΔP, one can determine how systems react to pressure changes and how those changes influence work done on or by the system.
Δt: Δt represents the change in time, which is a crucial concept in understanding motion and physical processes. This term highlights the difference between two specific time points, enabling the calculation of rates such as speed and velocity. It also plays a vital role in analyzing thermal processes and energy transfer by showing how time intervals affect the behavior of materials and systems.
ΔU: ΔU represents the change in internal energy of a system, which is a key concept in thermodynamics. It describes how energy is transferred within a system due to heat and work interactions. Understanding ΔU helps explain how energy conservation principles apply to physical processes, highlighting the relationship between energy input, output, and the resulting state of the system.
ΔV: ΔV, or change in volume, is a fundamental concept in physics that describes the difference in volume between two states or conditions of a system. This term is particularly relevant in the context of thermal expansion of solids and liquids, as well as the first law of thermodynamics and its associated processes.