Question:

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is:

Updated On: May 2, 2025

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The Correct Option is B

Approach Solution - 1

In the context of thermodynamics, an ideal gas can undergo several types of processes, each defined by how certain parameters change:

Adiabatic Process: No heat exchange occurs (Q = 0). The process is characterized by a steeper curve on a PV diagram compared to an isothermal process.
Isothermal Process: Temperature remains constant (ΔT = 0). The PV curve follows a hyperbola, defined by PV = nRT.
Isobaric Process: Pressure remains constant (ΔP = 0). The PV curve is a horizontal line.
Isochoric Process: Volume remains constant (ΔV = 0). The PV curve is a vertical line.

In the provided figure (unavailable for reference here), we need to identify the curve representing the adiabatic process. Generally, an adiabatic process in an ideal gas follows the equation:

P*V^γ = constant

where γ (gamma) is the heat capacity ratio (C_p/C_v). The curve for the adiabatic process is steeper compared to the isothermal curve (because γ > 1 for ideal gases).

Given the provided options:

A: Typically less steep
B: The steepest curve
C: A likely candidate for isothermal (flatter curve)
D: A likely candidate for isobaric or isochoric

The process that appears to be the steepest, and thus corresponds to the adiabatic process, is option B.

Therefore, the adiabatic process is represented by curve 2.

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Approach Solution -2

Understanding the PV diagram:

The figure in the question shows a pressure (P) vs volume (V) graph for an ideal gas undergoing four different thermodynamic processes starting from the same initial point.

Here's how each type of process behaves on a PV diagram:

Adiabatic process: Steeper curve than isothermal. No heat exchange occurs. Follows the equation PV^γ = constant (γ > 1).
Isothermal process: A gentler curve compared to adiabatic. Follows the equation PV = constant.
Isochoric process: Vertical line (constant volume, changing pressure).
Isobaric process: Horizontal line (constant pressure, changing volume).

By observing the figure:

Curve 4 is a vertical line → Isochoric
Curve 1 is a horizontal line → Isobaric
Curve 3 is a smooth downward curve → Isothermal
Curve 2 is the steepest downward curve → Adiabatic

Therefore, the adiabatic process corresponds to curve B.

Conclusion: The correct answer is Option 2 (Curve 2) as it represents the adiabatic process.

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Concepts Used:

Thermodynamics

Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.

Important Terms

System

A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.

There are three types of systems:

Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.

Thermodynamic Process

A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.

There are four types of thermodynamic process that have their unique properties, and they are:

Adiabatic Process – A process in which no heat transfer takes place.
Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
Isobaric Process – A process in which no change in pressure occurs.
Isothermal Process – A process in which no change in temperature occurs.

Laws of Thermodynamics

Zeroth Law of Thermodynamics

The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.

First Law of Thermodynamics

The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.

Second Law of Thermodynamics

The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.

Third Law of Thermodynamics

Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.