Question:

In an adiabatic expansion of an ideal gas the product of pressure and volume

Updated On: Apr 2, 2025
  • Decreases
  • Increases
  • Remains constant
  • At first increases and then decreases
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The Correct Option is A

Solution and Explanation

In an adiabatic process, no heat is exchanged with the surroundings. According to the first law of thermodynamics and for an ideal gas undergoing adiabatic expansion, the product of pressure and volume, \( P \cdot V \), decreases. This is because, as the gas expands, its pressure decreases and its volume increases, but the rate at which the volume increases is slower than the pressure decreases, leading to an overall decrease in the product of \( P \) and \( V \).

So, the correct answer is (A): Decreases

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Concepts Used:

Kinetic Molecular Theory of Gases

Postulates of Kinetic Theory of Gases:

  • Gases consist of particles in constant, random motion. They continue in a straight line until they collide with each other or the walls of their container. 
  • Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases.
  • Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision.  No energy is lost or gained from collisions. The time it takes to collide is negligible compared with the time between collisions.
  • The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and
    kinetic energy of the gas refer to the average of these speeds.
  • The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move.
  • All gases at a given temperature have the same average kinetic energy.
  • Lighter gas molecules move faster than heavier molecules.