Cyclic Process

Introduction

Let us take a container containing air and start heating that container. Let the initial temperature and pressure of the air 25°C and 1 atmospheric pressure, respectively. After heating for some time, the temperature of the air will become 100°C and the pressure of the air 2 atmospheric pressure. So the temperature and pressure of the air tells us the state of the air at that particular time. And this temperature and pressure is the thermodynamic variable which is defining or fixing the state of the air.

So we can say that the state of any thermodynamic system can be specified by thermodynamic variables, that is, its pressure, temperature, volume, number of moles. The variable may be extensive or intensive in nature.

Now when we have heated that container containing air, then its state changes from 25°C and 1 atmospheric pressure to 100°C and 2 atmospheric pressure. But it cannot happen suddenly, it must take some time. In between the final and initial state, it has gone through infinite states. If each and every state is defined, then we join all those states.

Thermodynamic Process

This process of change of state by the change in thermodynamic variables (like pressure, volume, temperature, number of moles, etc.) is called Thermodynamic process.

This is only possible if the pressure of the air remains the same throughout the process. Let us assume that the initial pressure, temperature and volume of the air is 1 atmospheric pressure, 27°C (ambient temperature) and 1 $\mathrm{m^3}$, respectively and after heating the final pressure, temperature and volume will be 1 atmospheric pressure, 50°C and $\mathrm{2m^3}$, respectively. Now after removing the burner, the air starts cooling and decreases its temperature and volume. After some time, the state of the air will be the same as that of ambient i.e., 1 atmospheric pressure, 27°C (ambient temperature) and 1 $\mathrm{m^3}$. So we can say that the air returns to its state.

Some of the important processes are as listed below -

• Isothermal process
• Adiabatic process
• Isobaric process
• Isochoric process
• Cyclic and non-cyclic process
• Reversible and irreversible process

In this tutorial we will study about the Cyclic process and its properties in detail. Let us start the Cyclic process.

Cyclic Process

Cyclic processes are those processes in which the initial and final state of the process will be the same.

Let us understand this statement with the help of an example.

Suppose we have a piston cylinder arrangement containing air inside it as shown in figure

• Start heating the base of that piston cylinder arrangement with the help of a burner and assume that all the heat is utilized for the upward movement of the piston and for increasing the temperature of the air.

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Figure -1

Yes, it may be possible that the path acquired by both processes will be different but the initial and final state will be the same in the cyclic processes.

Cyclic Process and State Functions

As we have studied, state functions are those which do not depend on the path and only depend on the initial and final state. It is also called the point function. One of the best examples of the state function is the internal energy. So the internal energy (U) depends only on the initial and final state.

Now as we know that in the cyclic processes the initial and final state will be the same. So the change in the internal energy ($\Delta$U) will be zero in the case of a cyclic process.

So, ($\Delta$U)= 0

Now we know that according to the first law of thermodynamics -

$\mathrm{\Delta Q\:=\:\Delta U\:+\:W\:\:…. (1)}$

where, $\mathrm{\Delta Q}$ = Change in heat energy

W = Work done

Now if, ($\Delta$U)= 0 then we can write equation (1) as -

$\mathrm{\Delta Q\:=\:W\:\:…. (2)}$

So from the equation (2), we can say that for a cyclic process the total heat energy is converted in the work done.

Work Done in Cyclic Processes

As we know that the work done can be calculated by calculating the area enclosed by the process and the axis containing volume as a variable on PV diagram, that is, on Pressure-Volume diagram. So in the case of a closed path, the work will be the area enclosed by that closed path on the PV diagram. So for a cyclic process also, the work done will be the area of the closed path. Since the work done and heat exchange is equal in case of cyclic process then that area will also give the heat exchange.

Also, if the cycle follows the clockwise path then the work done will be positive i.e., the work is done by the system. But if the cycle follows the counter-clockwise path then the work done will be negative that is, work is done on the system as shown in the figure 2.

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Figure -2

Carnot Cycle

One of the very famous examples of cyclic processes is the Carnot Cycle. The Carnot cycle consists of four processes, namely:

• Reversible Isothermal Expansion

• Reversible Adiabatic Expansion

• Reversible Isothermal Compression

• Reversible Adiabatic Compression.

With the help of these four processes the Carnot cycle completes as shown in the figure 3.

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Figure -3

Conclusion

It can be concluded that Cyclic processes are reversible processes, but the vice versa is not true, that is, all reversible processes are not cyclic processes.

FAQs

Q1. What is a cyclic process?

Ans. Cyclic processes are those in which the initial and final state of the process will be the same.

Q2. Give some examples of thermodynamic processes.

Ans. Few examples of Thermodynamics processes are -

• Isothermal process
• Adiabatic process
• Isenthalpic process
• Isobaric process

Q3. What will be the change in internal energy of an ideal gas in a cyclic process?

Ans. For an ideal gas, the change in internal energy will be zero in a cyclic process.

Q4. How can the work done in a cyclic process be calculated?

Ans. The work done in a cyclic process will be the area enclosed by the closed path on a PV diagram.

Q5. Give one example of the Cyclic process.

Ans. The Carnot engine is one of the best examples of cyclic processes.