Efficiency of a Carnot engine

Question

A Carnot engine operates between temperatures of $ 600 \, \text{K} $ and $ 300 \, \text{K} $. If it absorbs $ 900 \, \text{J} $ of heat from the source, how much work does it perform?

Answer 1

Step 1: Understanding the Concept:
This question asks about the factors that determine the efficiency of a Carnot engine, which is a theoretical, ideal reversible heat engine.
Step 2: Key Formula or Approach:
The thermal efficiency ($\eta$) of a heat engine is defined as the ratio of the work output (W) to the heat input from the source ($Q_H$): $\eta = \frac{W}{Q_H}$. For a Carnot engine operating between two heat reservoirs at absolute temperatures $T_H$ (the hot source) and $T_C$ (the cold sink), the efficiency is given by the specific formula: \[ \eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H} \] Step 3: Detailed Explanation:
From the formula $\eta = 1 - T_C/T_H$, we can see that the efficiency of a Carnot engine depends only on the absolute temperatures of the hot source and the cold sink. Let's analyze the options:
(A) "depends on the nature of the working substance" - This is false. Carnot's theorem states that all reversible engines operating between the same two temperatures have the same efficiency, regardless of the working substance.
(B) "does not depend on the nature of the working substance" - This is true, as explained above.
(C) "depends only on the temperature of the source" - This is false; it also depends on the sink temperature.
(D) "depends only on the temperature of the sink" - This is false; it also depends on the source temperature.
(E) "does not depend on both temperature of the source...and sink" - This is false; it depends on precisely these two temperatures.
Step 4: Final Answer:
The efficiency of a Carnot engine does not depend on the nature of the working substance.

Efficiency of a Carnot engine

Show Hint

The Correct Option is B

Solution and Explanation

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