# I am not sure i solved right I got 400

• Jun 10th 2007, 06:40 AM
jaycas21
I am not sure i solved right I got 400
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
• Jun 10th 2007, 07:52 AM
topsquark
Quote:

Originally Posted by jaycas21
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

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

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

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

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