3.6 Adiabatic Processes for an Ideal Gas
3 min read•june 24, 2024
Adiabatic processes are key to understanding thermodynamics in ideal gases. These processes occur without heat exchange, causing changes as the gas expands or compresses. Unlike processes, adiabatic ones follow a unique equation relating and .
Applications of the are widespread in physics and engineering. By using this equation and the law, we can solve problems involving pressure, volume, and temperature changes in adiabatic transitions. This knowledge is crucial for analyzing real-world systems like engines and refrigeration cycles.
Adiabatic Processes for an Ideal Gas
Temperature changes in adiabatic processes
Top images from around the web for Temperature changes in adiabatic processes
4.5 The Carnot Cycle – University Physics Volume 2 View original
Is this image relevant?
Adiabatic process - Wikipedia View original
Is this image relevant?
3.6 Adiabatic Processes for an Ideal Gas – University Physics Volume 2 View original
Is this image relevant?
4.5 The Carnot Cycle – University Physics Volume 2 View original
Is this image relevant?
Adiabatic process - Wikipedia View original
Is this image relevant?
1 of 3
Top images from around the web for Temperature changes in adiabatic processes
4.5 The Carnot Cycle – University Physics Volume 2 View original
Is this image relevant?
Adiabatic process - Wikipedia View original
Is this image relevant?
3.6 Adiabatic Processes for an Ideal Gas – University Physics Volume 2 View original
Is this image relevant?
4.5 The Carnot Cycle – University Physics Volume 2 View original
Is this image relevant?
Adiabatic process - Wikipedia View original
Is this image relevant?
1 of 3
- involves no heat exchange between the system and its surroundings, system is thermally isolated
- causes temperature decrease as is done by the gas, decreasing (expanding gas in a piston)
- causes temperature increase as is done on the gas, increasing (compressing gas in a piston)
- Change in temperature directly related to change in volume, greater volume change leads to greater temperature change (doubling volume causes significant cooling)
- Adiabatic processes can be reversible if performed slowly enough to maintain
Adiabatic vs isothermal processes
- Isothermal process occurs at constant temperature with pressure and volume inversely proportional, following [PV = constant](https://www.fiveableKeyTerm:PV_=_constant)
- On a PV diagram, isothermal process appears as a hyperbola (curve with asymptotes)
- occurs with no heat exchange, pressure and volume related by adiabatic condition equation , is
- On a PV diagram, adiabatic process has steeper slope than isothermal process (more vertical line)
- For same volume change, adiabatic process results in greater pressure change than isothermal process (more significant pressure increase or decrease)
- Adiabatic processes more efficient than isothermal processes in terms of work done (more work output for same volume change)
- Adiabatic processes can be considered a specific type of
Applications of adiabatic condition equation
- Adiabatic condition equation relates pressure , volume , and ratio of specific heats
- For ideal , (helium)
- For ideal , (nitrogen)
- Solving adiabatic transition problems:
- Identify initial and final states of the system
- Use adiabatic condition equation to relate initial and final states: , subscripts 1 and 2 denote initial and final states
- If necessary, use law to relate pressure, volume, and temperature
- Example problem: Ideal monatomic gas undergoes , doubling its volume. Given initial pressure and volume , find final pressure
- Solution:
- for monatomic gas
- , final pressure significantly lower than initial pressure
- Solution:
Thermodynamic considerations
- remains constant in a reversible adiabatic process
- Quasi-static processes occur slowly enough for the system to remain in thermodynamic equilibrium at each step
- Thermodynamic equilibrium is maintained when all parts of the system have uniform properties and are not changing with time
Key Terms to Review (35)
Absolute temperature scale: An absolute temperature scale is a thermodynamic temperature scale that uses absolute zero as its null point. The two most common absolute temperature scales are Kelvin and Rankine.
Adiabatic Compression: Adiabatic compression is a thermodynamic process in which a gas or fluid is compressed without the transfer of heat to or from the surroundings. This means that the system undergoes a change in pressure, volume, and temperature, but there is no net heat exchange with the environment.
Adiabatic Condition Equation: The adiabatic condition equation describes the relationship between the pressure, volume, and temperature of an ideal gas undergoing an adiabatic process, where no heat is exchanged with the surroundings. This equation is a fundamental principle in the study of thermodynamics and is particularly relevant in the context of adiabatic processes for an ideal gas.
Adiabatic expansion: Adiabatic expansion is a process in which a gas expands without exchanging heat with its surroundings. During this expansion, the internal energy of the gas decreases, resulting in a drop in temperature.
Adiabatic Expansion: Adiabatic expansion is a thermodynamic process in which a system exchanges no heat with its surroundings, meaning that all the work done by or on the system comes from or is converted to a change in the system's internal energy. This concept is particularly important in the study of ideal gases and the second law of thermodynamics.
Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings. In such processes, changes in internal energy are solely due to work done by or on the system.
Adiabatic Process: An adiabatic process is a thermodynamic process in which no heat is transferred to or from the system. In other words, the system is thermally isolated from its surroundings, and any changes in the system's internal energy are due solely to work done on or by the system.
Coefficient of volume expansion: The coefficient of volume expansion is a material-specific constant that quantifies the fractional change in volume per degree change in temperature. It is typically denoted by $\beta$ and measured in $\text{K}^{-1}$.
Diatomic Gas: A diatomic gas is a gas composed of molecules that contain two atoms of the same element, such as hydrogen (H2), oxygen (O2), and nitrogen (N2). These gases are characterized by their unique properties and behavior, particularly in the context of adiabatic processes for an ideal gas.
Entropy: Entropy is a measure of the disorder or randomness in a system. It quantifies the number of possible microscopic configurations that correspond to a thermodynamic system's macroscopic state.
First law of thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed in an isolated system, only transformed from one form to another. It is also known as the law of energy conservation.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy can be transformed from one form to another, but it cannot be created or destroyed. It establishes the fundamental principle of energy conservation, which is crucial for understanding heat transfer, thermodynamic systems, and adiabatic processes in an ideal gas.
Heat Capacity Ratio: The heat capacity ratio, also known as the adiabatic index or the isentropic expansion factor, is a dimensionless quantity that describes the relationship between the heat capacity at constant pressure and the heat capacity at constant volume for an ideal gas. This ratio is a crucial parameter in the analysis of adiabatic processes for an ideal gas.
Ideal gas: An ideal gas is a hypothetical gas that follows the ideal gas law, where its particles do not interact except through elastic collisions and occupy no volume. This model simplifies the study of gases by assuming perfectly random motion and no intermolecular forces.
Ideal Gas: An ideal gas is a theoretical model of a gas that follows a simple set of physical laws. It is a useful concept in thermodynamics and statistical mechanics to understand the behavior of real gases under various conditions.
Ideal gas model: The ideal gas model is a theoretical framework that simplifies the behavior of gases, assuming that they consist of a large number of particles that are in constant, random motion and that they do not interact with one another except during elastic collisions. This model helps explain the relationships between pressure, volume, and temperature for an ideal gas, allowing for predictions about gas behavior under various conditions, particularly in adiabatic processes where no heat is exchanged with the surroundings.
Internal energy: Internal energy is the total energy contained within a system due to both the random motions of its particles and the potential energies of their interactions. It encompasses kinetic and potential energy at the microscopic level.
Internal Energy: Internal energy is the total energy contained within a thermodynamic system, consisting of the kinetic energy of the system's particles and the potential energy associated with the configuration of the particles. It is a fundamental concept in thermodynamics that describes the energy stored within a system, which can be altered through the processes of work and heat transfer.
Isobaric: Isobaric refers to a process or condition in which the pressure remains constant. This term is particularly relevant in the context of adiabatic processes for an ideal gas, where the pressure-volume relationship is a key factor in understanding the behavior of the gas.
Isothermal: Isothermal refers to a process or condition in which the temperature remains constant while heat is transferred into or out of a system. In an isothermal process, the system's internal energy does not change because any heat added to the system is balanced by an equal amount of work done by the system, allowing it to maintain a steady temperature throughout.
Monatomic Gas: A monatomic gas is a gas composed of individual, uncombined atoms rather than molecules. These atoms move independently and do not form chemical bonds with each other, resulting in unique thermodynamic properties compared to molecular gases.
Open System: An open system is a thermodynamic system that exchanges both energy and matter with its surroundings. It is a system that is not isolated from the external environment and can interact with it by transferring heat, work, and/or mass across the system boundary.
Polytropic Process: A polytropic process is a thermodynamic process that follows the relation $$PV^n = ext{constant}$$, where P is pressure, V is volume, and n is the polytropic index. This type of process generalizes various specific thermodynamic processes, including isothermal and adiabatic processes, and describes how an ideal gas changes states under different conditions of heat transfer.
Pressure: Pressure is the force exerted per unit area on a surface, commonly measured in pascals (Pa). It plays a critical role in understanding how gases behave, how thermal expansion affects materials, and how energy transfers occur in systems. Pressure influences how gases expand or compress, impacts thermodynamic processes, and governs the interactions between molecules at the microscopic level.
PV = constant: The term 'PV = constant' refers to the relationship between pressure (P) and volume (V) in an adiabatic process for an ideal gas. This relationship states that the product of pressure and volume remains constant during an adiabatic process, where no heat is exchanged with the surroundings.
PV^γ = constant: PV^γ = constant is a fundamental relationship in thermodynamics that describes the behavior of an ideal gas undergoing an adiabatic process. It states that the product of the pressure (P) and the volume (V) raised to the power of the adiabatic index (γ) remains constant during an adiabatic change of state for an ideal gas.
Ratio of Specific Heats: The ratio of specific heat capacity at constant pressure (C_p) to specific heat capacity at constant volume (C_v) for an ideal gas. This ratio, often denoted as gamma (γ), is a dimensionless quantity that provides important information about the thermodynamic properties of a gas.
Reversible process: A reversible process is a thermodynamic process that can be reversed without leaving any net change in either the system or the surroundings. These processes are ideal and occur infinitesimally slowly, allowing the system to remain in equilibrium throughout.
Reversible Process: A reversible process is a thermodynamic process that can be reversed without leaving any trace on the surroundings. In other words, a reversible process can be undone, and the system and the surroundings can be returned to their initial states without the expenditure of any work or the absorption of any heat from the surroundings.
Temperature: Temperature is a measure of the average kinetic energy of the particles (atoms or molecules) in a substance. It quantifies the degree of hotness or coldness of an object and is a fundamental concept in thermodynamics that is closely related to the transfer of heat energy.
Thermodynamic Equilibrium: Thermodynamic equilibrium is a state in which the macroscopic properties of a system, such as temperature, pressure, and chemical composition, do not change over time. It is a fundamental concept in thermodynamics that underpins the study of energy transformations, work, heat, and the behavior of systems.
Volume: Volume is a fundamental physical quantity that describes the three-dimensional space occupied by an object or a substance. It is a measure of the amount of space enclosed within a defined boundary or container.
Work: Work is the energy transferred to or from an object via a force acting upon it over a displacement. In physics, work is mathematically expressed as $W = F \cdot d \cdot \cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between them.
Work: Work is a fundamental concept in physics that describes the transfer of energy due to the application of a force over a distance. It is a measure of the energy expended or transferred during a physical process and is a crucial factor in understanding the behavior of thermodynamic systems, electric potential, and the storage of energy in capacitors.
γ: The Greek letter gamma (γ) is a dimensionless quantity that represents the ratio of specific heats of a gas, also known as the adiabatic index or adiabatic exponent. It is a fundamental parameter in the study of adiabatic processes for an ideal gas, which describe changes in a system's pressure, volume, and temperature without the exchange of heat with the surroundings.