Question

The work done in an adiabatic change in an ideal gas depends upon:

• A. change in its pressure
• B. change in its volume
• C. change in its specific heat
• D. change in its temperature

Hint:

In adiabatic processes, the work done depends on the change in volume and the specific heat ratio \( \gamma \).

Answer 1

The Correct Option is B

An adiabatic process involves an ideal gas undergoing changes without heat exchange with its surroundings. The work performed during such a process is understood through the adiabatic process equation: PV^γ = constant, where P denotes pressure, V represents volume, and γ (gamma) is the adiabatic index or specific heat ratio (C_p/C_v).

The work done (W) in an adiabatic process is given by the relation: W = (P₁V₁ - P₂V₂) / (γ - 1).

Leveraging the adiabatic condition, work done can also be expressed in terms of the volume change: W = (C_v(T₁ - T₂))/(1-γ).

Relating work done directly to volume change yields: W = ((P₁V₁ - P₂V₂))/(γ - 1)) = K(V₂^1-γ - V₁^1-γ)/(1-γ).

Consequently, the work done in an adiabatic change is directly dependent on the gas's volume. Therefore, the work done in an adiabatic change is determined by the change in its volume.