What are (a) W_out and Q_H and (b) the thermal efficiency for the heat engine shown in FIGURE EX21.14?

검증된 단계별 안내

Step 1: Understand the problem. The heat engine operates between two reservoirs, absorbing heat (QH) from the hot reservoir and performing work (Wₒᵤₜ) while expelling heat (QC) to the cold reservoir. The thermal efficiency (η) is defined as the ratio of work output to heat input: η = Wₒᵤₜ / QH.

Step 2: Identify the given values from FIGURE EX21.14. Extract the values for QH (heat absorbed from the hot reservoir) and QC (heat expelled to the cold reservoir). These values are typically provided in the figure or accompanying text.

Step 3: Calculate the work output (Wₒᵤₜ) using the first law of thermodynamics for a heat engine: Wₒᵤₜ = QH - QC. Subtract the heat expelled (QC) from the heat absorbed (QH).

Step 4: Determine the thermal efficiency (η) using the formula η = Wₒᵤₜ / QH. Divide the work output (Wₒᵤₜ) by the heat input (QH) to find the efficiency of the engine.

Step 5: Express the thermal efficiency as a percentage by multiplying the result by 100: η (%) = (Wₒᵤₜ / QH) × 100. This gives the efficiency in a more interpretable form.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Work Output (Wₒᵤₜ)

Work output (Wₒᵤₜ) refers to the useful work produced by a heat engine during its operation. It is calculated as the difference between the energy input from the heat source and the energy rejected to the heat sink. This concept is crucial for evaluating the performance of the engine, as it directly relates to the engine's ability to convert thermal energy into mechanical energy.

Heat Input (QH)

Heat input (QH) is the total amount of thermal energy absorbed by the heat engine from the heat source during one complete cycle. This energy is essential for the engine's operation, as it provides the necessary energy to perform work. Understanding QH is vital for calculating the thermal efficiency of the engine, as it serves as the baseline for comparing the work output.

Thermal Efficiency

Thermal efficiency is a measure of how effectively a heat engine converts heat energy into work. It is defined as the ratio of the work output (Wₒᵤₜ) to the heat input (QH), often expressed as a percentage. A higher thermal efficiency indicates a more effective engine, and it is a key performance indicator in thermodynamics, helping to assess the effectiveness of different engine designs.