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

In an adiabatic process, an ideal gas changes without exchanging heat with the surroundings. The work done in such a process can be understood by looking at the equation for an adiabatic process:

PV^γ = constant,

where P is the pressure, V is the volume, and γ (gamma) is the adiabatic index or specific heat ratio (C_p/C_v).

The work done (W) in an adiabatic process can be expressed by the relation:

W = (P₁V₁ - P₂V₂) / (γ - 1).

Using the adiabatic condition, one can also express the work done in terms of the change in volume:

The relation simplifies to:

W = (C_v(T₁ - T₂))/(1-γ)

However, directly relating work done to volume change:

W = ((P₁V₁ - P₂V₂))/(γ - 1)) = K(V₂^1-γ - V₁^1-γ)/(1-γ)

Thus, it is clear that the work done depends directly on the volume of the gas during the adiabatic change. Therefore, the correct choice regarding what the work done depends upon in an adiabatic change is: change in its volume.