First slide

Heat Engine; Carnot Engine and refrigerator

Question

One of the most efficient engines ever developed operates between 2100 K and 700 K. It’s actual efficiency is 40%, what percentage of it’s maximum possible efficiency is?

Moderate

A

40%
B

60%
C

66.67%
D

33.3%

Solution

$\begin{array}{rcl} p e r c e n t a g e e f f i c i e n c y o f h e a t e n g i n e i s η & = & \frac{T_{h o t} - T_{c o l d}}{T_{h o t}} x 100 - - - (1) \\ g i v e n T_{h o t} & = & 2100 K, \\ T_{c o l d} & = & 700 K \\ s u b s t i t u t e g i v e n v a l u e s i n a b o v e e q u a t i o n (1) \\ η & = & \frac{2100 - 700}{2100} \times 100 \\ η & = & \frac{1400}{2100} \times 100 \\ η & = & \frac{200}{3} %, t h i s i s m a x i m u m p o s s i b l e e f f i c i e n c y o f t h e e n g i n e \\ g i v e n a c t u a l e f f i c i e n c y i s 40 % \\ p e r c e n t a g e o f a c t u a l e f f i c i e n c y \\ w i t h r e s p e c t t o m a x i m u m p o s s i b l e e f f i c i e n c y i s & = & \frac{a c t u a l e f f i c i e n c y}{m a x i m u m e f f i c i e n c y} x 100 \\ = & \frac{40}{\frac{200}{3}} x 100 \\ p e r c e n t a g e o f a c t u a l e f f i c i e n c y \\ w i t h r e s p e c t t o m a x i m u m p o s s i b l e e f f i c i e n c y & = & 60 % \end{array}$

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