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(D) The efficiency of a Carnot engine operating between the boiling point $(T_1 = 373 \ K)$ and freezing point $(T_2 = 273 \ K)$ of water is given by

Vedclass · Accepted Answer

Statement $1$ is true,Statement $2$ is true,Statement $2$ is the correct explanation of Statement $1.$

Vedclass · Answer

(D) The efficiency of a Carnot engine operating between the boiling point $(T_1 = 373 \ K)$ and freezing point $(T_2 = 273 \ K)$ of water is given by $\eta = 1 - \frac{T_2}{T_1}$.Substituting the values: $\eta = 1 - \frac{273}{373} = 1 - 0.732 = 0.268$ or $26.8\%$.Since the maximum possible efficiency (Carnot efficiency) is $26.8\%$,an engine with $30\%$ efficiency is impossible. Thus,Statement $1$ is true.Statement $2$ is a fundamental principle of thermodynamics (Carnot's theorem),which states that no engine can be more efficient than a Carnot engine operating between the same two temperatures. This theorem explains why the inventor's claim in Statement $1$ is impossible. Therefore,Statement $2$ is the correct explanation of Statement $1$.

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