Adiabatic Process

Introduction

Every matter in the universe is made up of small particles called molecules. According to the distance between the molecules and the attractive force, they are classified. Different matters have different properties. The properties of matter include mass temperature, density, volume pressure, etc. The transformation of heat is done in matters by conduction, convection, and radiation. Thermodynamics deals with the thermal energy which comes from heat. Thermodynamics comes under the branch of physics which explain the relation of heat, work, and temperature with energy, entropy. Now, we are going to discuss the thermodynamic system, process, adiabatic process and their applications.

Thermodynamic system

A matter which is confined in a particular space by the boundaries is called a thermodynamic system. There occurs both internal transformations and also to the exterior through the boundaries. They have definite permeability. According to their boundaries they may be classified as closed systems, open systems, and isolated systems. In an isolated system, there is no transformation of energy or matter across the boundaries of the system. There is no work done on the system. In a closed system, there is a transformation of energy but the matter cannot be transferred across the boundaries. Example: a cylinder closed by a valve. In an open system, there is a free exchange of energy and matter across boundaries. Example: pool filled with water.

Thermodynamic processes

In thermodynamic processes there is an exchange of energy between the system or from the system to the surroundings associated with the change in volume, pressure, or temperature. In this process, there is energy transmission and also work done on the system or by the system. The processes are classified into four according to different ways and different conditions that it is carried out. These processes are isothermal, isobaric, isochoric, and adiabatic. In an isothermal process, the heat is allow to exchange with environment but the temperature of the system remains constant throughout the process. In an isobaric process, the pressure of the system remains constant throughout the process. In an isochoric process, there is no change in the volume of the system throughout the process.

What is an adiabatic process?

In this process, there is no exchange of heat energy is not allowed within and out of the system. Some conditions should be maintained for an adiabatic process. One is that the system should be completely isolated from the surroundings. The next one is that it should take place in a short time then only there is sufficient time for the heat transfer. The expansion and contraction of gas are adiabatic. The equation for the adiabatic process is

$\mathrm{PV^{\gamma}  = constant}$

$\mathrm{PV^{\gamma}  = k}$

Here P denotes the pressure of the system

V denotes the volume of the system.

$\mathrm{\gamma = C_P/C_V}$    denotes the proportion of the specific heat capacity at constant pressure to the constant volume.

Work done in adiabatic process

Consider a cylinder whose walls are made of insulating material and associated with a frictionless piston which is also insulating material. Let us assume that one mole of gas is filled inside the cylinder. Let us take the initial and final values of pressure, volume, and temperature (P1, V1, T1) and (P2, V2, T2). Work done in an adiabatic change from (P₁, V₁, T₁) to (P₂, V₂, T₂) is

$$\mathrm{W = \int_{v_1}^{v_2} P\: dv}$$

$$\mathrm{P = \frac{k}{V^ \gamma}}$$

$$\mathrm{W = \int_{v_1}^{v_2} \frac{k}{V^ \gamma} dv}$$

$$\mathrm{W = k \int_{v_1}^{v_2} \frac{1}{V^ \gamma} dv}$$

$$\mathrm{W = \int_{v_1}^{v_2} V^ \gamma dv}$$

As

$$\mathrm{\int x^n dx = \frac{x^{n+1}}{n+1} = k[\frac{V^{− \gamma + 1}}{− \gamma + 1}]^{v_2}_{v_1}}$$

By applying the upper and lower limit we get,

$$\mathrm{W = \frac{k}{−\gamma+1}[V_2^{−\gamma + 1} − V_1^{−\gamma + 1} ]}$$

$$\mathrm{W = \frac{k}{−\gamma+1}[V_2^{−\gamma + 1} − kV_1^{−\gamma + 1} ]}$$

As $\mathrm{P_1 (V_1)^{\gamma}  = P_2 (V_2)^{\gamma} = k}$, we can write

$$\mathrm{W = \frac{1}{− \gamma + 1}[P_2 V_2^{\gamma}V_2^{−\gamma + 1} − P_1 V_1^{\gamma} V_1^{−\gamma + 1}]}$$

$$\mathrm{W = \frac{1}{− \gamma + 1}[P_2 V_2^{−\gamma + 1 + \gamma} − P_1 V_1^{−\gamma + 1 + \gamma}]}$$

$$\mathrm{W = \frac{1}{− \gamma + 1}[P_2 V_2 − P_1 V_1]}$$

$$\mathrm{W = \frac{1}{\gamma − 1}[P_1 V_1 − P_2 V_2]}$$

From an ideal gas $\mathrm{P_1 V_1 = mRT_1}$ and $\mathrm{P_2 V_2 = mRT_2}$

$$\mathrm{W = \frac{mRT_1 − mRT_2}{\gamma − 1}}$$

$$\mathrm{W = mR[\frac{T_1 − T_2}{\gamma − 1}]}$$

This is the work done in an adiabatic process.

Reversible adiabatic process

In this process, a system can return to its original state without any change. It cannot be achieved experimentally. An idealized reversible adiabatic process does not exist in nature. It is also called an isentropic process. Ex: adiabatic expansion of a real gas.

Irreversible adiabatic process

The adiabatic process is said to be irreversible if the system is not able to return to its original. There occurs a change in entropy of the system. Example: heat transfer.

Application of adiabatic process

Some of the applications of adiabatic equations are given below.

• Adiabatic process is applied in refrigerators.

• In thermal heat engines part of it uses the adiabatic process.

• Compressors and turbines are also the applications of adiabatic processes.

• Igloo box and thermos flasks also use the principle of the adiabatic process.

• A quantum harmonic oscillator applies the adiabatic process.

Conclusion

In this tutorial, the thermodynamics system, and process, work done in adiabatic processes was discussed. The thermodynamic system is also classified as open and closed sytem. The working of a thermodynamic system is depends on the thermodynamic variables like temperature, pressure and volume. And occurrence of different processes like isothermal, isobaric, isochoric and adiabatic in different systems is also depends on the these thermodynamic variables. In an adiabatic process no heat change is take place with its environment. Because of this feature, it is used in heat pumps and refrigerators. The reversible and irreversible processes and the application of adiabatic processes were also cover in this tutorial.

FAQs

Q1. Give some examples for all thermodynamic processes.

Ans: The thermodynamic processes are of four types and they are isothermal, adiabatic, isobaric, and isochoric processes. Examples are water while boiling, refrigerator, Carnot engine, heat pump, freezing of water into ice, pressure cooker, and vertical airflow in the atmosphere.

Q2. Differentiate isothermal and adiabatic processes.

Ans: 

Isothermal process	Adiabatic process
The heat energy is transferred in and out of the system	There is no transfer of heat energy in the system
Constant temperature	Varied temperature
Slow transformation takes place	Fast transformation takes place

 Q3. What is the specific heat capacity?

Ans: The quantity of heat energy given to the system to increase the temperature of the material whose mass is one mole to one degree is called specific heat capacity.

Q4. How the temperature is varying with adiabatic compression and expansion?

Ans: During adiabatic compression, the temperature of the system increases. During adiabatic expansion, the temperature of the system decreases.

Q5. What is the first law of thermodynamics?

Ans: In a closed system the internal energy of the system is given by the difference between the heat and the work done by the system. This is known as the first law of thermodynamics.

Q6. What do you mean by isothermal and isobaric processes?

Ans: In an isothermal process, the temperature is fixed only heat is allow to change. whereas in isobaric, pressure is constant throughout the process.