An adiabatic process is a thermodynamic process in which there is no transfer of heat between a system and its surroundings. In other words, no heat enters or leaves the system during the process. This can occur if the process happens very rapidly or if the system is well-insulated so that heat cannot flow in or out. Because there is no heat transfer, the change in the internal energy of the system is solely due to work done on or by the system. Adiabatic processes are often characterized by changes in pressure, volume, and temperature of the system. Adiabatic processes are commonly found in various natural phenomena and engineering applications. For example, the compression and expansion of gases in a piston-cylinder arrangement without significant heat exchange with the surroundings can be considered adiabatic processes. Additionally, the rapid rise or descent of air parcels in the atmosphere often approximates adiabatic conditions.
If the gas is compressed adiabatically, work is done on the gas. So, Wadia is negative and the change in internal energy is positive (i.e. internal energy of gas increases). The gas heats up during adiabatic compression and T1 < T2.
Equation for adiabatic process PVγ = constant TVγ – 1 = constant Tγ p1 – γ = constant
The adiabatic process is a thermodynamic process in which the pressure, volume, and temperature of the system change, but there is no exchange of heat between the system and the surroundings.
In a rapid and instantaneous process, such as an adiabatic one, there isn't ample time for heat exchange to occur, thus rendering the process adiabatic.
1.0Definition of Adiabatic Process
An adiabatic process is defined as a thermodynamic process during which there is negligible or no exchange of heat between the system and its surroundings.
This can occur either because the process happens so quickly that there is no time for heat exchange, or because the system is well-insulated, preventing any heat transfer. As a result, the change in internal energy of the system during an adiabatic process is solely due to work done on or by the system.
2.0Equation of Adiabatic Process
The equation of an adiabatic process depends on the context, particularly whether the process is reversible or irreversible. For an ideal gas undergoing an adiabatic process, the equation is given by:
γ is the adiabatic constant or ratio of specific heats
•Cp is the specific heat at constant pressure
•Cv is the specific heat at constant volume.
For an ideal monatomic gas, γ=35
For an ideal diatomic gas, γ=57
This equation reflects the conservation of energy in an adiabatic process, where no heat is exchanged with the surroundings, so the change in internal energy (ΔU) is entirely due to work done on or by the gas.
3.0Work Done in Adiabatic Process
Let initial state of system is (P1, V1, T1) and after adiabatic change final state of system is (P2, V2, T2) then we can write P1V1=P2V2=K(here K is constant)
It means the work done by an ideal gas during adiabatic expansion (or compression) is on the cost of change in internal energy proportional to the fall (or rise) in the temperature of the gas.
If the gas expands adiabatically, work is done by the gas. So, Wadia is positive.
The gas cools during adiabatic expansion and T1 > T2.
If the gas is compressed adiabatically, work is done on the gas. So, Wadia is negative.
The gas heats up during adiabatic compression and T1 < T2.
4.0Graphs in Adiabatic Process
Slope of the adiabatic curve
For an adiabatic process, PVγ = constant
Differentiating, γPVγ – 1 dV + Vγ dP = 0
⇒ Vγ dP = –γPVγ – 1 dV
⇒ dVdP=−VγγPVγ−1=−γVP=γ(−VP)
Slope of adiabatic curve,
[dVdP]adiabatic =−VγP
The magnitude of the slope of the adiabatic curve is greater than the slope of the isotherm
dVdPadiabatic =γVP=γdVdPisothermal ⇒ slope of isothermal changes slope of adiabatic changes =γ
Since γ is always greater than one so an adiabatic curve is steeper than an isothermal curve.
5.0Solved Examples of Adiabatic Process
A gas enclosed in a thermally insulated cylinder fitted with a non–conducting piston. If the gas is compressed suddenly by moving the piston downwards, some heat is produced. This heat cannot escape from the cylinder. Consequently, there will be an increase in the temperature of the gas.
If a gas is suddenly expanded by moving the piston outwards, there will be a decrease in the temperature of the gas.
Bursting of a cycle tube.
Propagation of sound waves in a gaseous medium.
In diesel engines, burning of diesel without a spark plug is done due to adiabatic compression of diesel vapour and air mixture.
Example:
The temperature and pressure of air in the tyre tube are 27°C and 8 atm, respectively. If the tube suddenly bursts, then calculate the final temperature of the air. [γ = 1.5)
Solution:
⇒ P11−γT1γ=P21−γT2γ⇒(8)1−γ(300)γ=(1)1−γ(T2)γ
⇒ T2 = 150 K ⇒ T2 = 150 – 273 = – 123°C
Example:
A diatomic ideal gas is compressed adiabatically to 321 of its initial volume. If the initial temperature of the gas is T1K and final temperature is aT1 then find the value of a.