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Isobaric Process - Definition, Thermodynamic Changes During an Isobaric Process, P vs V plot, T vs V Plot, Work Done, Practice Problems and FAQs

Isobaric Process - Definition, Thermodynamic Changes During an Isobaric Process, P vs V plot,  T vs V Plot, Work Done, Practice Problems and FAQs

Have you cooked noodles? The instructions give the proportions of water to be used against the contents of the packet. But we seldom measure out the water accordingly. To be on the safer side we add more water than asked for. The cooked noodles become watery. Now, what do you do for removing the excess water to relish noodles?

You continue heating in an open vessel for some more time till the excess water is removed. This open process of heating is an example of an isobaric process.

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Come, let us know more about not cooking but about the isobaric process.

Table of Content

  • Definition of Isobaric Process
  • Thermodynamic Changes During an Isobaric Process
  • Pressure vs Volume (P vs V) Plot for an Isobaric Process
  • Temperature vs Volume (T vs V) Plot for Isobaric Process
  • Work done in Isobaric Process
  • Practice Problems
  • Frequently Asked Questions (FAQs)

Definition of an Isobaric Process

It is a thermodynamic process in which the system experiences the same pressure throughout the process from initial to final. Consider the noodle case, the vessel is heated with no lids. The noodles and the water inside are under the atmospheric pressure of 1 atmosphere throughout the heating till you remove the vessel from the heater.

All natural process takes place at constant atmospheric pressure conditions.

You also can have a process, in a closed system, but with a movable lid. Initially, the lid is under atmospheric pressure. Heating increases the pressure inside the vessel which will push up the lid. The lid moves up, and stops at a place where the pressure inside equals the external atmospheric pressure, thus maintaining the pressure inside, a constant, ie same as atmospheric pressure.

Such process happening under the same pressure conditions is referred to as constant pressure or isobaric processes.

In the isobaric process, there will be no change in the system pressure with variation in temperature, which means that there is zero change in pressure (dP) over the course of the process.

 P = constant, i.e.,  Pi = Pf

dP = 0 or ΔP = 0

Thermodynamic Changes During an Isobaric Process

An illustration is given in the figure below to understand the thermodynamic changes happening during an isobaric process. Consider the process at a micro level, where the gas particles start moving with a greater speed on increasing the temperature as their kinetic energy increases. Further, this increases the collision frequency of the gas particles and also the impact per collision. Therefore, with the increase in the temperature the volume increases and the piston goes up.

Now, if the process is seen at a macro level, then the pressure exerted by the gas molecules (Pgas) virtually remains constant. However, overall, the volume of a gas increases with the increase in temperature. When the overall expansion of gas is divided into infinitesimal (i.e., very small) expansions, the piston remains stationary after each of these expansions, indicating that the external atmospheric pressure (Patm) is balanced by the internal pressure exerted by the gas particles (Pgas).

Pressure vs Volume (P vs V) Plot for an Isobaric Process

The pressure vs volume plot for an isobaric process is given in the figure below. On increasing the temperature, the gas is expanding from Vi to Vf by maintaining a constant pressure as shown in the graph. However, on decreasing the temperature, the gas will compress by maintaining a constant pressure.

P

V

Temperature vs Volume (T vs V) Plot for an Isobaric Process

In the illustration discussed above for the thermodynamic changes in the isobaric process (Fig. below), it was observed that the volume occupied by the gas particles increases with the increase in temperature, i.e., the temperature is directly proportional to volume.

T ∝ V or T = kV

f

T

Ti

vi

vf

This can be correlated with the equation of a straight line.

y = mx + c

T = kV

If the above two equations are compared, the y-intercept (c) would be zero and with a slope (m) = k on a T-V curve.

In the case of expansion of gas at isobaric conditions, as the temperature of the gas increases, the volume occupied by the gas also increases. During compression, the temperature of the gas decreases and will result in a subsequent decrease in volume.

Work Done in Isobaric Processes

W=dW=-PextdV(i)

From the illustration of the isobaric process which is discussed above in this article, it was observed that for the piston to remain stationary, the external atmospheric pressure is to be balanced by the pressure exerted by the gas particles and thus, maintaining a constant pressure, i.e., Pext=Pgas

Thus, the equation (i) becomes;

W=-PgasdV=-PgasdV

Integrating from initial volume (Vi) to final volume (Vf), we get;

W = - Pgas ViVf dV

W = - Pgas(VfVi)

So, W = - Pgas(ΔV)

This formula for work done can be applied for isobaric reversible as well as irreversible processes.

All reactions carried out at atmospheric pressure are examples of isobaric processes.

Calculation of Work Using P-V Graph

Work done on the gas is basically the area under the P-V curve. As pressure remains constant in the isobaric process, so area will be the product of constant pressure and change in volume as shown below.

Practice Problems

Q1. Choose an isobaric process from the following

  1. Boiling of water
  2. Freezing of water
  3. Reversible expansion of an ideal gas
  4. All of them

Answer: (D)

Solution: The process of turning water into steam or ice is an illustration of the isobaric reaction. During boiling the temperature remains the same at 100°C and the pressure also is the same as the atmospheric pressure of one atmosphere. But the volume of the water increases from going liquid to vapour.

In the reversible expansion of an ideal gas at constant temperature increase in volume has to decrease the pressure. Freezing of water is an isothermal process.

Q2. In which process the P-V indicator diagram is a straight line parallel to the volume axis?

  1. Isothermal
  2. Isochoric
  3. Isobaric
  4. None

Answer: (C)

Solution: The pressure vs volume plot for an isobaric process is given in Figure below. On increasing the temperature, the gas is expanding from Vi to Vf by maintaining a constant pressure as shown in the graph.

Q3. A gas expands at a constant pressure of 5 atm from 5L to 10L. The work done by the gas is:

  1. - 25 atm L
  2. 25 atm L
  3. - 5 atm L
  4. 5 atm L

Answer: (A)

Solution: As the process is occurring at constant pressure, hence it is an isobaric process and formula for calculating the work done in an isobaric process is:

W = - Pgas(ΔV)

Now,

ΔV = (10-5) = 5L

So,

W = - Pgas(ΔV) = - 5 × (5) = - 25 atm L

Q4. A gas expands at constant pressure as shown below. The work done by the gas is:

  1. - 10 atm L
  2. 10 atm L
  3. - 15 atm L
  4. - 5 atm L

Answer: Option A

Solution: Work done by the gas is basically area under the P-V curve. As the process is occurring as constant pressure, hence it is an isobaric process and work done in an isobaric process is PV.

Now, work done = Area of rectangle ABCD = (AD x AB) = (2 x 5) = 10 atm L

As volume is increasing which means expansion is taking place and hence work done will be negative as work is done by the gas which is -10 atm L .

Frequently Asked Questions(FAQs)

Q1. What conditions are needed for a process to be isobaric?
Answer:
A thermodynamic process known as an isobaric process occurs under constant pressure. Temperature, volume, and internal energy are not constant in this process, even though the pressure is constant.

Q2. Is there any heat transfer that occurs during the isobaric process?
Answer:
Heat enters the system during an isobaric expansion process. The system uses some of the heat to work on the environment, while the rest of the heat is used to increase the internal energy.

Q3. Can a procedure that is isobaric be reversed?
Answer:
Processes that take place under constant pressure are called isobaric processes. So, certainly, we may perform the isobaric process slowly and reversibly if we are able to regulate the change in other macroscopic characteristics of the system so that they change slowly enough.

Q4. Is freezing isobaric in nature?
Answer:
During the freezing of liquid state to solid state, the temperature of the system remains constant and hence is known as the isothermal process. The freezing process involves a volume change though very small and hence will be accompanied by a pressure though negligible change. So, freezing is not an isobaric process.

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