First slide

Heat engine

Question

A Carnot engine has efficiency 25%. It operates between reservoirs of constant temperatures with
temperature difference of 80 K. What is the temperature of the low temperature reservoir?

Moderate

A

$- 25^{0} C$
B

$25^{0} C$
C

$- 33^{0} C$
D

$33^{0} C$

Solution

Efficiency of a Carnot engine, i.e.
$η = 1 - \frac{T_{2}}{T_{1}} = \frac{T_{1} - T_{2}}{T_{1}}$
$\Rightarrow \frac{25}{100} = \frac{T_{1} - (T_{1} - 80)}{T_{1}}$
$\Rightarrow \frac{1}{4} = \frac{80}{T_{1}} \Rightarrow T_{1} = 320 K$
$T_{1} = 320 - 273 = 47^{\circ} C$
Temperature of the low temperature reservoir
$= 47 - 80 = - 33^{\circ} C$

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