Question 835: Thermodynamics & KTG

Question

A Carnot engine has the same efficiency between (i) $$100 \mathrm{~K}$$ and $$600 \mathrm{~K}$$ and (ii) $$\mathrm{T} \mathrm{K}$$ and $$960 \mathrm{~K}$$. The temperature $$\mathrm{T}$$ in kelvin of the sink is

Accepted Answer

Efficiency of a carnot engine is $$\eta=1-\frac{T_C}{T_H}$$
For case (i),
$$\mathrm{T}_{\mathrm{C}}=100 \mathrm{~K}$$ and $$\mathrm{T}_{\mathrm{H}}=600 \mathrm{~K}$$
$$	herefore \quad \eta_1=1-\frac{100}{600}=\frac{5}{6}$$
For case (ii),
$$\mathrm{T}_{\mathrm{C}}=\mathrm{T} \mathrm{K} 	ext { and } \mathrm{T}_{\mathrm{H}}=960 \mathrm{~K}$$
$$	herefore \quad \eta_2=1-\frac{\mathrm{T}}{960}$$
Given $$\eta_1=\eta_2$$
$$\begin{aligned}
	herefore \quad \frac{5}{6} & =1-\frac{\mathrm{T}}{960} \
\frac{5}{6} & =\frac{960-\mathrm{T}}{960}
\end{aligned}$$
Solving for $$\mathrm{T}$$, we get $$\mathrm{T}=160 \mathrm{~K}$$

Answer

120

Answer

160

Answer

240

Answer

320

Thermodynamics & KTG

A Carnot engine has the same efficiency between (i) $100 \mathrm{~K} and 600 \mathrm{~K} and (ii) \mathrm{T} \mathrm{K} and 960 \mathrm{~K}. The temperature \mathrm{T}$ in kelvin of the sink is

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