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 Sub Topics A thermodynamic process can be explained by different parameters such as pressure, temperature, volume etc. One of the important process in thermodynamics is adiabatic process. The term "adiabatic" literally means impassable or impermeable. One can prevent heat flow either by surrounding the system with thermally insulating material or by carrying out the process so quickly that there is not enough time for appreciable heat flow.

During an adiabatic process, the working substance is perfectly insulated from the surroundings. It can neither give heat nor take heat from the surroundings.

An adiabatic process is a thermodynamic process in which pressure, volume and temperature of the system change but there is no exchange of heat between the system and the surrounding.

Q = 0

Q = 0

$\Delta$ E = Q + W = W

## Work done in Adiabatic Process

dQ = dU + dW

In an adiabatic process, no exchange of heat is allowed between the system and the surrounding.

dQ = 0
$\therefore$ dU + dW = 0

or dW = -dU

but dU = $C_{v}$dT

Where, $C_{v}$ is the molar specific heat of gas at constant volume.

dW = -$C_{v}$dT

Let $W_{adia}$ be the work done when the gas expands adiabatically from temperature $T_{1}$ to temperature $T_{2}$.

Then, $W_{adia}$ = $-\int_{T_{1}}^{T_{2}}C_{v}dT$

= $-C_{v}\int_{T_{1}}^{T_{2}}dT$

= $-C_{v}[T]_{T_{1}}^{T_{2}}$

= $-C_{v}[T_{2}-T_{1}]$

or

$W_{adia}$ = $C_{v}[T_{2}-T_{1}]$

Which is the expression for the work done for one mole of an ideal gas during adiabatic process.

Now, $C_{p} – C_{v} = R$

Where $C_{p}$ is the molar specific heat at constant pressure and $R$ is the molar gas constant.

Dividing both sides by $C_{v}$, we get

$\frac{C_{p}}{C_{v}}- \frac{C_{v}}{C_{v}}$ = $\frac{R}{C_{v}}$

$\gamma - 1$ = $\frac{R}{C_{v}}$

$C_{v}$ = $\frac{R}{\gamma -1}$

So, $W_{adia}$ = $C_{v}[T_{2}-T_{1}]$ = $\frac{R}{\gamma -1}$$[T_{2}-T_{1}]$

Which is another expression for the work done during adiabatic process.

A process that is reversible and adiabatic is called an adiabatic reversible process. Adiabatic systems are thermally insulated systems so they do not let out or let in heat during the process. A reversible process is a process wherein quantity of heat transferred is directly proportional to the systems entropy change. Since there is no entropy change, the heat transferred is zero. Thus this process is an adiabatic reversible process. These processes are also called is an entropic processes.

A process involving heat transfer is called adiabatic process. Additionally, an adiabatic process that is irreversible is an isenthalpic process. This process extracts no work. In an adiabatic reversible process dQ=TdS = 0. That is the change in entropy is zero. The increase in disorder resulting from the gas occupying a greater volume is exactly balanced by the decrease in disorder associated with the lowered temperature and reduced molecular speed.

Adiabatic reversible process is applied in the designing of insulated walls, in adiabatic flame temperature. An insulated wall acts as adiabatic boundary that does not allow heat transfer; becomes impermeable; the system is called to be adiabatically insulated. In case of adiabatic flame temperature the flame is adiabatic; it attains the temperature with zero heat loss to the surroundings. This temperature is called adiabatic flame temperature.

An adiabatic reversible process cannot take place under normal temperature and pressure. This process is only a thermodynamic concept. This process can be constructed for an ideal gas enclosed in a cylinder with adiabatic walls. This system is fitted with a piston that slides without friction under special circumstances of pressure and temperature. Thus the above examples are not truly adiabatic reversible processes; they only tend to be adiabatic and reversible.

Entropy of a body undergoing an adiabatic process must increase or, in the limit of a reversible adiabatic process, remain constant.

For an irreversible adiabatic process, the entropy of a body always increases regardless of whether energy is transferred to or from the body as work during the process. The entropy of a body can be decreased only through energy transfer from the body as heat. Hence, for a body undergoing an adiabatic process,

$dQ = 0$ is not equal to TdS

i.e.,$dS > 0$, Entropy change is greater than zero.