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Graphical Comparison of Thermodynamic Processes

Graphical Comparison of Thermodynamic Processes

Shivani PooniaUpdated on 02 Jul 2025, 06:32 PM IST

Thermodynamics is the area of physics dealing with heat and other types of energy. In particular, thermodynamics explains how thermal energy is transformed into and from other kinds of energy, and its interrelation with matter. Any thermodynamic process is a process of energy transfer within a system or between systems. The properties of a thermodynamic process are pressure, temperature, and volume. The state of the system at the present time is called the thermodynamic state of a system. An excellent example of a thermodynamic process is when food stays cool inside a refrigerator. A refrigerator removes the heat from the inside compartments and transfers it to the air on the outside.

This Story also Contains

  1. Constant Volume Process
  2. Work done during the process:
  3. Constant Pressure Process:
  4. Some Solved Examples
  5. Summary
Graphical Comparison of Thermodynamic Processes
Graphical Comparison of Thermodynamic Processes

Constant Volume Process

Representation on P-V diagram:

This process is represented on the P-V diagram by a vertical straight line as shown in the figure, since V1=V2.

Work done during the process:

W=∫V1V2Pdv

But dv=0 for an isochoric process

∴W=0

Thus, work done during the constant volume process is zero which is also evident from the P-V diagram as no area is enclosed by the vertical line on the P-V diagram.

Constant Pressure Process:

Representation on P-V diagram:

During this process the pressure or the gas remains constant therefore it is represented by a horizontal line on the P-V diagram. See figure.

Work done during the process:


W=∫V1But P is constant.
∴ Work done =P∫V1V2dv=P(V2−V1)

A rectangle on P-V diagram represents the work done by the gas during the constant pressure process.

Recommended topic video on (Graphical Comparison of Thermodynamic Processes)


Some Solved Examples

Example 1: One mole of an ideal gas expands from state X to Y by three paths 1, 2, and 3 as shown in the figure below. If W1, W2, and W3 are respective work done by ideal gas along the three paths then:

1)W1=W2=W3

2)W3>W1>W2

3) W3>W2>W1

4)W1>W2>W3

Solution

Work is a path function and not a state function. The area under P-V curve gives Work done. As far as the magnitude is concerned, work done by gas will be maximum in path 3 because the area under the curve is highest in the case of path 3. The second highest area is under path 2 and the least area is of curve 1.
Hence, Option number (3) is correct

Example 2: The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is

1) 489Correct)

2)85

3)58

4)54

Solution

W=(8−2)2+12((12−8)×(8−2))W=48

Example 3: What is the relation between the temperatures in the below graph which represents an isothermal expansion of gas at different temperatures?

1)T1>T2>T3

2)T2>T3>T1

3) T3>T2>T1

4)No relationship can be established

Solution

In the isothermal process, Temperature is constant.
Also, we know for an ideal gas, PV=nRT

As we can see T is constant, so we can say PV=k (here k is constant).

This equation of PV=k represents the equation of a hyperbola.

The higher the value of k the farther the curve is from the origin. So we can conclude that
T3>T2>T1
Hence, Option number (3) is correct

Example 4: Find out the magnitude of work (in kJ) done by one mole of an ideal gas for expansion.

1)-1

2)2

3) 6

4)60

Solution

Work is a path function and not a state function and the area under the P-V curve gives work.

So, work will be the total area of the Trapezium

∴∣ work |=12×( sum of parallel sides )×( distance between the parallel sides )∴∣ work |=12×6×20=60×10−5 bar − lit ∴∣ work ∣=60×105 bar − lit =60×105×10−3 bar −m3=6000 J

Thus, the magnitude of work done is 6 kJ

Example 5: One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is_________ J (nearest integer )

1) 6

2)7

3)4

4)6.5

Solution

I→II→ Isobaric II→III→ Isochoric III→I→ Isothermal WI−II=−1[40−20]=−20 Lit atm WII−III=0 WIV-I =2.303nRtlog⁡V2 V1

=2.303PVlog⁡V2 V1=2.303(1×20)log⁡2=2.303×20×0.3010=13.818

W total =−20+13.818=(−6.182 lit atm )=6.182 lit atm

Summary

It's an interesting area of physics that deals mainly with the interaction of different kinds of energy, especially heat. How it describes the transformation of thermal energy into other forms of energy and how it influences the matter is quite interesting.
A thermodynamic process can be said to be a transfer of energy either within or between systems. The properties of the system in consideration are considered significant in these processes. The values of such properties at any given time describe the thermodynamic state of the system. An elementary example of a thermodynamic process could be the heating of water in a kettle. The heat from the surroundings—the stove—is transferred and absorbed by the kettle's system, which raises the temperature of the water.


Frequently Asked Questions (FAQs)

Q: What can the slope of an isotherm at different points on a P-V diagram tell us about a substance's compressibility?
A:
The slope of an isotherm at different points on a P-V diagram indicates the isothermal compressibility of the substance. A steeper negative slope suggests lower compressibility, meaning the substance resists volume changes when pressure is applied. A shallower slope indicates higher compressibility. The variation in slope across the diagram can reveal how a substance's compressibility changes under different pressure an
Q: How does the behavior of a van der Waals gas differ from an ideal gas on a P-V diagram?
A:
On a P-V diagram, a van der Waals gas shows significant deviations from ideal gas behavior, especially at high pressures and low temperatures. The curves are less hyperbolic and show a more complex shape. At low temperatures, they exhibit a region where pressure increases with volume (unstable region), which is not seen in ideal gases. This difference arises from accounting for molecular size and intermolecular attractions in the van der Waals equation.
Q: What information can be derived from the spacing between isobars on a T-V diagram?
A:
The spacing between isobars on a T-V diagram provides information about the thermal expansion coefficient of the substance. Wider spacing indicates a larger volume change for a given temperature change at constant pressure, implying a higher thermal expansion coefficient. Conversely, closer spacing suggests a lower thermal expansion coefficient. This spacing can vary for different substances and can change in different regions of the diagram, reflecting changes in material properties.
Q: How can you use a P-V diagram to illustrate the concept of internal energy changes?
A:
While internal energy changes are not directly shown on a P-V diagram, they can be illustrated by considering the area under the curve (work) and the heat added or removed. For a closed system, the change in internal energy is the sum of heat added and work done on the system. By showing different paths between two states and considering the areas under these paths, you can demonstrate how different combinations of heat and work can lead to the same internal energy change.
Q: What is the significance of the ideal gas law curve on a P-V diagram?
A:
The ideal gas law curve on a P-V diagram is a hyperbola (PV = constant) that represents the behavior of an ideal gas at constant temperature. It serves as a reference for comparing real gas behavior. Deviations from this curve indicate non-ideal behavior due to factors like intermolecular forces and molecular size. The ideal gas curve is crucial for understanding gas behavior under various conditions and for developing more complex models.
Q: How can you use a P-V diagram to illustrate the concept of path dependence in thermodynamics?
A:
Path dependence can be illustrated on a P-V diagram by showing different paths between two states. While state functions (like internal energy) depend only on the initial and final states, path functions (like work and heat) depend on the specific path taken. By drawing different curves between two points on the diagram, you can show how the area under each curve (representing work) differs, demonstrating that work is path-dependent.
Q: How can you use a P-V diagram to illustrate the concept of a heat engine?
A:
A heat engine can be illustrated on a P-V diagram as a closed loop representing a cyclic process. The clockwise direction of the cycle indicates that net work is done by the system. The area enclosed by the loop represents the net work output per cycle. Different parts of the loop can represent different processes (e.g., isothermal expansion, adiabatic compression), allowing visualization of how the engine converts heat into work.
Q: What does the area between two different process curves on a P-V diagram represent?
A:
The area between two different process curves on a P-V diagram represents the difference in work done between the two processes. If the processes start and end at the same points, this area shows the net difference in work. This concept is crucial in comparing the efficiency of different thermodynamic cycles or in understanding the advantages of one process over another in terms of energy transfer.
Q: How can you use a P-V diagram to explain the concept of thermodynamic stability?
A:
Thermodynamic stability can be explained using a P-V diagram by examining the shape of isotherms. In stable regions, isotherms have a negative slope (∂P/∂V < 0), indicating that an increase in pressure leads to a decrease in volume, which is mechanically stable. Regions with positive slopes are unstable and can lead to phase transitions. The inflection points of isotherms, where the curvature changes, indicate the limits of stability.
Q: What can the tangent to a curve on a P-V diagram tell us about the process?
A:
The tangent to a curve on a P-V diagram provides information about the instantaneous rate of change of pressure with respect to volume at that point. The slope of the tangent indicates how quickly pressure is changing with volume. A horizontal tangent suggests a turning point or extremum in the process, while the sign of the slope indicates whether pressure is increasing or decreasing with volume change.
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