Which one of the following is applicable for an adiabatic expansion of an ideal gas?

CONCEPT:

Adiabatic Expansion of an Ideal Gas

• An adiabatic process is one in which no heat is exchanged between the system and its surroundings.
• For an ideal gas undergoing adiabatic expansion, the change in internal energy (ΔE) is equal to the work done (ΔW).
• Since there is no heat exchange (Q = 0), the first law of thermodynamics can be written as:

  ΔE = Q - ΔW

  ΔE = 0 - ΔW

  ΔE = -ΔW

EXPLANATION:

• In an adiabatic expansion:

  ΔE = -ΔW

• Therefore, the work done by the system (ΔW) is equal to the negative change in internal energy (ΔE).
• Thus, for adiabatic expansion of an ideal gas:
  • ΔW = ΔE

Therefore, the correct answer is option 2: ΔW = ΔE.