A Carnot engine is operated between two heat reservoirs at temperatures of 520520520 K and 300300300 K. How much mechanical work is performed by the engine during each cycle?

Ch 20: The Second Law of Thermodynamics

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 20: The Second Law of Thermodynamics

문제 14b

20장, 문제 14b

A Carnot engine is operated between two heat reservoirs at temperatures of $520$ K and $300$ K. How much mechanical work is performed by the engine during each cycle?

검증된 단계별 안내

Understand the concept of a Carnot engine: A Carnot engine is an idealized heat engine that operates on the reversible Carnot cycle. It is the most efficient engine possible between two heat reservoirs.

Identify the given temperatures: The high-temperature reservoir (T1) is at 520 K, and the low-temperature reservoir (T2) is at 300 K.

Calculate the efficiency of the Carnot engine using the formula: $ \eta = 1 - \frac{T2}{T1} $. Substitute the given temperatures into this formula to find the efficiency.

Relate the efficiency to work and heat: The efficiency $ \eta $ is also defined as the ratio of the work done by the engine (W) to the heat absorbed from the high-temperature reservoir (Q1), i.e., $ \eta = \frac{W}{Q1} $.

To find the mechanical work performed (W), rearrange the efficiency formula to $ W = \eta \times Q1 $. You will need the value of Q1, the heat absorbed from the high-temperature reservoir, to calculate W.

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주요 개념

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

Carnot Engine

A Carnot engine is a theoretical thermodynamic cycle that operates between two heat reservoirs, achieving maximum efficiency. It is an idealized model that assumes no energy losses due to friction or other inefficiencies, and its efficiency depends solely on the temperatures of the heat reservoirs.

Thermodynamic Efficiency

Thermodynamic efficiency of a heat engine is defined as the ratio of work output to heat input. For a Carnot engine, this efficiency is determined by the temperatures of the hot and cold reservoirs, calculated using the formula: Efficiency = 1 - (T_cold/T_hot), where temperatures are in Kelvin.

Mechanical Work in Thermodynamics

Mechanical work in thermodynamics refers to the energy transferred by the system to its surroundings during a cycle. In the context of a Carnot engine, the work done is the useful energy output, calculated by multiplying the efficiency by the heat absorbed from the hot reservoir during each cycle.