When there is no exchange of heat between the system and the surroundings, the process is known as adiabatic process. It is an integral part of thermodynamics. The concept of adiabatic process is a fundamental principle in physics which deals with the behaviour of gases.
By understanding the concept of the adiabatic process, students get an idea about work, heat, and internal energy. This article provides insight on important topics like what is an adiabatic process, the work done by an adiabatic process derivation, daily life examples of adiabatic processes, adiabatic expansion and compression, and types of adiabatic processes.
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Define adiabatic process: There is no heat exchange in an adiabatic process in thermodynamics, neither during an adiabatic expansion nor compression. An adiabatic process is one in which, both irreversibility and reversibility are possible. The following conditions must be met for an adiabatic reaction to occur:
Insulation must be perfect between the system and its surroundings. It is important to carry out the process rapidly. The turbines are great examples of adiabatic systems. During the adiabatic process, the work done changes internal energy.
If
If
In terms of adiabatic processes, the following equation applies:
where,
According to the first law of thermodynamics,
For adiabatic process,
Let W work be done as the system goes from initial state
Work Done,
Using the adiabatic process formula,
By integrating both sides
We know that, constant
Simplifying we get,
Using ideal gas,
Substituting in (2), we get
where,
This is the work done by the adiabatic process equation.
Adiabatic compression causes a gas to increase in temperature, while adiabatic expansion, or a spring, causes the temperature to drop. An ideal gas, however, expands with isothermal heat.
In many practical situations, heat conduction through walls can be slow compared to the compression time of gas, because a piston compressing a gas contained inside a cylinder increases its pressure.
Generally, diesel engines make use of this to ignite the fuel vapor when there is little heat dissipation during an adiabatic process a compression stroke.
An adiabatically isolated system is cooled by decreasing the pressure on it, which allows it to expand and change its environment.
(i) Reversible Adiabatic Process
(ii) Irreversible Adiabatic Process
The area under the PV diagram of the adiabatic process gives the work done by the adiabatic process. The curve of the adiabatic process is steeper than that of the isothermal process.
Examples of adiabatic processes include:
The isothermal versus adiabatic process is explained in the table below:
Isothermal process |
Adiabatic process |
An isothermal process is defined as one of the thermodynamic processes which occur at constant temperature. |
An adiabatic process is defined as one of the thermodynamic processes that occur without any heat transfer between the system and the surroundings. |
Work done in an adiabatic process is due to the change in the net heat content in the system. |
Work done in the adiabatic process is due to the change in its internal energy. |
The temperature cannot be varied |
The temperature can be varied |
There is a transfer of heat |
There is no transfer of heat |
Also See,
Example 1: The work of 146 kJ is performed to compress one kilomole of gas adiabatically and in this process, the temperature of the gas increases by
1) monoatomic
2) diatomic
3) triatomic
4) a mixture of monoatomic and diatomic.
Solution:
Adiabatic Process
When a Thermodynamic System changes in such a way that no exchange of heat takes place.
1. Work Done Formula:
2. Plug in Values:
3. Compute Numerator:
4. Solve for
5. Find
Therefore, the corrected value of
Hence, the answer is the option (2).
Example 2: When a gas expands adiabatically
1) The system should allowed to expand slowly
2) Internal energy of gas is used in doing work
3) The law of conservation of energy does not hold
4) No energy is required for expansion
Solution:
1. No Heat Exchange: In an adiabatic process, there should be no exchange of heat between the system and surroundings, meaning
2. Sudden Compression or Expansion: For a process to be approximately adiabatic, it should occur quickly. This rapid change ensures that there is no time for heat to transfer, as in the case of a sudden burst of a tire.
Since
or
This means that if
Example 3: A given system undergoes a change in which the work done by the system equals the decrease in its internal energy. The system must have undergone an
1) Isothermal change
2) Adiabatic change
3) Isobaric change
4) Isochoric change
Solution:
In an adiabatic process:
According to the first law of thermodynamics:
For an adiabatic process, there is no exchange of heat between the system and its surroundings.
So,
This means the work done by the system equals the decrease in internal energy.
Hence, the answer is option 2.
Example 4: During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio CP/CV for the gas is
1)
2) 2
3)
4)
Solution:
or
From the adiabatic equation:
Using equations (1) and (2), we can equate the powers of
Solving this, we get:
or
Thus,
Hence, the answer is option (4).
Example 5: Two moles of an ideal monoatomic gas occupy a volume V at
Calculate (a) the final temperature of the gas and (b) the change in its internal energy.
Solution:
The equation of state for an adiabatic process is given by:
On solving this, we find:
For an adiabatic process, the relationship between temperature and volume is:
Given
or
Next, calculating the change in internal energy
This simplifies to:
Hence, the answer is the option 4.
When an adiabatic process occurs, the entire system's total heat remains constant.
During adiabatic compression, the temperature of a gas increases. This is because work is done on the gas, increasing its internal energy, and since no heat can escape (adiabatic), this energy increase manifests as a temperature rise.
During adiabatic expansion, the temperature of a gas decreases. This is because the gas does work on its surroundings, decreasing its internal energy, and since no heat can enter (adiabatic), this energy decrease results in a temperature drop.
In reality, no process can be perfectly adiabatic because some heat transfer is always present. However, processes that occur very quickly or in well-insulated systems can be approximated as adiabatic for practical purposes.
The compression and expansion of air in sound waves is an approximately adiabatic process. The pressure changes occur so rapidly that there's little time for heat transfer, making the process nearly adiabatic.
In an adiabatic process, no heat is exchanged with the surroundings, while temperature may change. In an isothermal process, temperature remains constant, but heat can be exchanged with the surroundings.
Yes, temperature can change during an adiabatic process. In fact, temperature usually does change because no heat is exchanged with the surroundings, so any work done by or on the system directly affects its internal energy and temperature.
For the same initial and final volumes, the work done in an adiabatic process is generally different from an isothermal process. In an adiabatic process, temperature changes, affecting the pressure-volume relationship, while in an isothermal process, temperature remains constant.
In an adiabatic process, pressure and volume are related by the equation PV^γ = constant. This means that as volume decreases, pressure increases more rapidly than in an isothermal process (where PV = constant).
γ (gamma) is the heat capacity ratio (Cp/Cv) of the gas. It determines how much the temperature changes for a given pressure or volume change in an adiabatic process. A higher γ means a greater temperature change for the same volume change.
The work done in an adiabatic process depends only on the initial and final states of the system, not on the path taken between these states. This is because no heat is exchanged, so the change in internal energy is solely due to work.
The Carnot cycle, which represents the most efficient possible heat engine, includes two adiabatic processes: adiabatic compression and adiabatic expansion. These processes connect the two isothermal processes in the cycle.
Adiabatic processes can be more efficient than non-adiabatic processes in certain applications because they don't lose energy to heat transfer. This is why rapid compression or expansion in engines is often approximated as adiabatic.
In a reversible adiabatic process, entropy remains constant because no heat is exchanged with the surroundings. However, in an irreversible adiabatic process, entropy increases due to internal friction or other irreversibilities.
A polytropic process is a thermodynamic process that follows the equation PV^n = constant, where n is the polytropic index. An adiabatic process is a special case of a polytropic process where n = γ (the heat capacity ratio).
For an adiabatic process, the first law of thermodynamics simplifies to ΔU = -W, where ΔU is the change in internal energy and W is the work done by or on the system. This is because Q (heat transfer) is zero in an adiabatic process.
The equation for an adiabatic process involving an ideal gas is PV^γ = constant, where P is pressure, V is volume, and γ (gamma) is the heat capacity ratio (Cp/Cv) of the gas.
In an adiabatic process, the change in internal energy of the system is equal to the negative of the work done by or on the system. If work is done on the system, internal energy increases; if the system does work, internal energy decreases.
In refrigerators and heat pumps, the rapid expansion of the refrigerant through the expansion valve is approximately adiabatic. This adiabatic expansion causes the refrigerant to cool, allowing it to absorb heat from the refrigerated space.
In a diesel engine, the initial compression of air in the cylinder is approximately adiabatic. This adiabatic compression raises the temperature of the air high enough to ignite the fuel when it's injected, without needing a spark.
In an adiabatic process, there is no heat transfer (Q = 0), so the change in enthalpy (H) is equal to the work done (W) plus the change in internal energy (ΔU). For an ideal gas, the enthalpy change in an adiabatic process is solely due to the temperature change.
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