The exhaust temperature of a Carnot heat engine is 350oC. What is the intake temperature if the efficiency is 25.0%?

400oC

543oC.

558oC

830oC

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- Jun 10th 2007, 06:40 AM #1

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- Jun 10th 2007, 07:52 AM #2
I presume you are talking about an exhaust temperature of 350 degrees C and not 3500 degrees C? For a Carnot engine:

$\displaystyle \epsilon = 1 - \frac{T_o}{T_i}$

where $\displaystyle \epsilon$ is the efficiency, $\displaystyle T_i$ is the intake temperature, and $\displaystyle T_o$ is the output (exhaust) temperature.

So

$\displaystyle \frac{T_o}{T_i} = 1 - \epsilon$

$\displaystyle T_o = T_i(1 - \epsilon)$

$\displaystyle T_i = \frac{T_o}{1 - \epsilon}$

So in your problem:

$\displaystyle T_i = \frac{350 \, ^oC}{1 - 0.25} = 466.667 \, ^oC$

-Dan