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Adiabatic Process Learn Formula, Definition, Derivation and Example
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Thermodynamics
In physics, the thermodynamic process describes how heat and energy move within a system.
One special type of process is the adiabatic process, where no heat is transferred between the system and its surroundings. This means the system changes in pressure, volume or temperature, but without gaining or losing heat. Adiabatic processes are important in topics like gas laws, engine cycles, and atmospheric studies, making them a key concept for students preparing for exams.
What is an Adiabatic Process?
An adiabatic process is when no heat is exchanged between a system and its surroundings.
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The word “adiabatic” comes from Greek, meaning “without heat transfer”. In this process, energy changes only as work, not heat. Key characteristics include rapid changes in pressure and temperature, as there’s no time for heat exchange. This can happen in situations like gas compression or when air cools as it rises in the atmosphere.
Adiabatic process- Key Concepts
In an adiabatic process, the system does not exchange heat with its surroundings (Q=0). This means that any change in the system’s energy comes from work done, rather than heat transfer.
The relationship between internal energy is crucial: when work is done or by the system, it directly affects the internal energy, causing changes in temperature or pressure. An isentropic process is a special case of adiabatic process where the process is also reversible, meaning there’s no loss of energy due to friction or other factors, and entropy remains constant. This typically happens in ideal conditions, like in a perfect gas undergoing adiabatic compression or expansion.
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Adiabatic Process Formula
In adiabatic conditions, all energy change happens through work, as there’s no heat transfer involved (Q=0). The pressure and volume of the system follow the relation PVr= constant, where
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γ (gamma) is the ratio of specific heats (Cp/Cv). This helps explain how gases behave during rapid compression or expansion. The work done can also be calculated using specific formulas based on whether the system expands or compresses, making these equations essential for solving adiabatic process problems. |
Derivation of Adiabatic Equation
To understand how pressure and volume are related in an adiabatic process, we derive the equation PV<sup>γ</sup> = constant. The equation shows that when no heat is exchanged the product of pressure (P) and volume (V) raised to the power of gamma(r) remains constant. Here r,(gamma) is the ratio of specific heats, defined as Cp/Cv, where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. This relationship is useful in solving numerical problems and understanding gas behaviour under adiabatic conditions. You can also visualise with the PV graph, where the adiabatic curve is steeper than the isothermal one.
Adiabatic Relation Between P, V, And T
We will be deriving the relation between P, V, and T using the first law of thermodynamics which states that heat supplied to the system is capable of doing some work when the heat absorbed by the system is equal to the sum of the increase in internal energy and external work done on the surrounding by the system.
An essential condition for the adiabatic process
- The system and surroundings must not be exchanging heat for which the walls should be insulated.
- The process of expansion and compression so that the system should not be able to exchange heat with the surroundings.
Case I: Relation between P and V
According to the First Law of thermodynamics
K: constant
This equation gives the relation between P( Pressure) and V( Volume ) of Ideal Gas.
Case II: Relation between P and T
We know that
PV = RT [ for one mole of gas ]
Substituting the value of V in the equation
This equation gives the relation between P and T.
Case III: Relation between V and T
We know that
PV = RT [ for one mole of gas ]
Substituting the value of P in the equation
This equation gives the relation between V (Volume) and T (Temperature).
Derivation of Work Done In Adiabatic Process
Go through the below derivation of work done in the Adiabatic process and
Let there be a cylinder that has insulated walls and has a frictionless and insulated piston. It contains gas inside it. Also, the gas expands adiabatically.
n: number of moles of an ideal gas
P: the pressure of a gas
dx: small distance moved by a piston
dW: work is done by gas
A: cross-sectional area of a piston
dV= Adx: increase in the volume of gas
P1, V1, T1: Initial state of Gas
P2, V2, T2: Final state of Gas
Total Work done of the gas is given by:
Also, we know that P1V1 and P2V2 are equal to nRT1 and nRT2 respectively. So the equation for work done in the adiabatic process is also given by
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What is an adiabatic process?
An adiabatic process is a thermodynamic process in which no heat exchange occurs between the system and its surroundings. In an adiabatic process, changes in pressure, volume, and temperature of the system occur without any transfer of heat.
How does an adiabatic process occur?
An adiabatic process occurs when a system is insulated, preventing any heat exchange with its surroundings. This can also occur if the process happens very quickly, not allowing sufficient time for heat transfer. In such a process, any change in the internal energy of the system is due to work done by or on the system.
What is the difference between an adiabatic process and an isothermal process?
In an adiabatic process, there is no heat transfer between the system and its surroundings, and thus the temperature of the system can change. However, in an isothermal process, the temperature of the system remains constant. This is because any change in internal energy due to work done is compensated by the heat transferred to or from the surroundings.
What is an example of an adiabatic process
A good example of an adiabatic process is the compression and expansion of air in a car's engine. When the air-fuel mixture in a cylinder is ignited, it expands rapidly and pushes the piston, doing work on it. This rapid expansion occurs so quickly that there is little to no time for heat to be exchanged with the surroundings.
What is the adiabatic equation?
For an ideal gas, the adiabatic process follows the equation PV^γ = constant, where P is the pressure, V is the volume, γ (gamma) is the heat capacity ratio (Cp/Cv), and 'constant' is a constant value. This equation indicates that, in an adiabatic process, as the volume of the gas increases, the pressure decreases, and vice versa, with the product of pressure and volume raised to the power γ remaining constant.