Question

How can the concept of maximum work be used to determine the efficiency of a thermodynamic cycle?

• A. By measuring the total heat input into the system.
• B. By calculating the work output as a fraction of the heat absorbed.
• C. By assessing the changes in volume at constant pressure.
• D. By analyzing the molecular interactions during the cycle.

Hint:

Thermodynamic Cycle Efficiency. Efficiency (\(\eta\)) = Net Work Output / Heat Input = \(W_{net / Q_{in\). This measures how effectively the heat input is converted into useful work.

Answer 1

The Correct Option is B

The thermal efficiency (\(\eta\)) of a thermodynamic cycle (like a heat engine) is defined as the ratio of the net work output (\(W_{net}\)) produced by the cycle to the amount of heat absorbed (\(Q_{in}\) or \(Q_H\)) from the high-temperature source during the cycle.
$$ \eta = \frac{\text{Net Work Output}}{\text{Heat Input}} = \frac{W_{net}}{Q_{in}} $$ The concept of maximum work arises in the context of the Carnot cycle, which represents the maximum possible efficiency achievable between two given temperature reservoirs (\(\eta_{Carnot} = 1 - T_C/T_H\)).
For any cycle, however, the efficiency is determined by comparing the actual work output obtained to the heat energy input required to achieve that work.
Option (2) correctly describes this fundamental definition of efficiency.
Measuring heat input alone (Option 1), volume changes (Option 3), or molecular interactions (Option 4) does not directly yield the efficiency.