Problem — Useful work for 1000 J absorbed

Problem

A Carnot engine operates between a hot source at $500\;\text{K}$ and a cold one at $300\;\text{K}$. Calculate the efficiency. How much work does it produce for every $1000\;\text{J}$ absorbed from the hot source?

Solution

Carnot efficiency.

$\eta_\text{Carnot} = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{500} = \ev{0{,}40 = 40\%}$

Useful work. From $\eta = L/Q_H$ we get $L = \eta\, Q_H$, with $Q_H = 1000\;\text{J}$:

$L = 0{,}40 \cdot 1000 = \ev{400\;\text{J}}$

Of the $1000\;\text{J}$ absorbed, $400\;\text{J}$ become work and the remaining $600\;\text{J}$ are released to the cold source.

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Topics: Macchine termiche Concepts: Ciclo di Carnot · Rendimento Skills: Impostazione simbolica Objects: Macchina termica