First slide

Heat Engine; Carnot Engine and refrigerator

Question

A carnot engine whose source is at 400 K takes 200 cal of heat and rejects 150 cal to sink. What is the temperature of sink?

Moderate

A

800 K
B

400 K
C

300 K
D

200 K

Solution

$\begin{array}{rcl} I n c a r n o t e n g i n e \\ s o u r c e t e m p e r a t u r e T_{1} =400 K (given) \\ a m o u n t o f h e a t g i v e n i s Q_{1} =200 cal \\ a m o u n t o f h e a t r e j e c t e d Q_{2} =150 cal \\ t e m p e r a t u r e o f \sin k i s T_{2} =? \\ w o r k d o n e b y e n g i n e i s {W=Q}_{1} {-Q}_{2} =200-150=50cal \\ s u b s t i t u t e g i v e n v a l u e s, \\ ⇒W=50 cal \\ e f f i c i e n c y i s η= \frac{W}{Q_{1}} \\ s u b s t i t u t e v a l u e s l e g i b l y \\ η= \frac{50}{200} = \frac{1}{4} \\ a n o t h e r e q u a t i o n f o r e f f i c i e n c y i n t e r m s o f t e m p e r a t u r e i s η=1- \frac{T_{2}}{T_{1}} \\ s u b s t i t u t e η v a l u e 1 / 4 i n a b o v e e q n \\ \frac{1}{4} & = & 1 - \frac{T_{2}}{400} \\ \Rightarrow & \frac{T_{2}}{400} = 1 - \frac{1}{4} = \frac{3}{4} \\ \Rightarrow & T_{2} =300 K=temperature of sink \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App