- The extensive quantity among the following is
(A) Pressure
(B) Temperature
(C) Chemical potential
(D) Volume
The extensive quantity in the given options is volume (D). Pressure, temperature and chemical potential are all intensive properties in thermodynamics.
Concept of extensive quantity
In thermodynamics, an extensive property is one that depends on the amount or size of the system.
If the system is divided into two equal parts, an extensive property (like volume, mass, internal energy) is divided accordingly and is additive over subsystems.
Intensive vs extensive properties
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Extensive properties:
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Depend on the quantity of matter (e.g. mass, volume, internal energy, entropy).
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Are additive: total value equals the sum of values for each part of the system.
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Intensive properties:
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Do not depend on system size (e.g. temperature, pressure, chemical potential).
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Remain the same when the system is divided into parts at equilibrium.
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Option-wise explanation
Option (A): Pressure
Pressure is defined as force per unit area.
If a system at uniform pressure is divided into two equal parts, each part has the same pressure as the original, so pressure does not scale with the amount of substance and is therefore an intensive property, not extensive.
Option (B): Temperature
Temperature measures the thermal state (degree of hotness) of a system and is uniform for a system in thermal equilibrium.
Dividing a system at uniform temperature into two parts leaves the temperature of each part unchanged, so temperature does not depend on the amount of matter and is an intensive property.
Option (C): Chemical potential
Chemical potential is the partial molar Gibbs free energy and represents the change in Gibbs free energy when an infinitesimal amount of a substance is added, at constant temperature and pressure.
It characterizes the system locally and remains the same for each part of a homogeneous system at equilibrium, so it is an intensive property.
Option (D): Volume
Volume is the space occupied by the system and increases directly with the amount of matter present.
If a system is divided into two equal parts, the total volume equals the sum of the volumes of the parts, so volume is additive and depends on system size, making it an extensive quantity; hence option (D) is correct.
Short exam-ready answer
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Pressure → intensive (independent of amount of substance).
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Temperature → intensive (same for all parts in thermal equilibrium).
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Chemical potential → intensive (defined per mole, characterizing local state).
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Volume → extensive (scales with amount of matter and is additive).
Therefore, among the given options, volume is the extensive quantity.
