First slide

Heat engine

Question

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{0} C$ , the efficiency of the engine is doubled. The temperatures of the source and sink are

Moderate

A

$80^{0} C, 37^{0} C$
B

$95^{0} C, 28^{0} C$
C

$90^{0} C, 37^{0} C$
D

$99^{0} C, 37^{0} C$

Solution

Initially $η = (1 - \frac{T_{2}}{T_{1}}) = \frac{W}{Q} = \frac{1}{6}$ --------------(i)
Finally $η^{'} = (1 - \frac{{T_{2}}^{'}}{T_{1}}) = (1 - \frac{(T_{2} - 62)}{T_{1}})$
= $1 - \frac{T_{2}}{T_{1}} + \frac{62}{T_{1}}$
= $η + \frac{62}{T_{1}}$ ---------------(ii)
It is given that $η^{'} = 2 η$ . Hence solving equations (i) and (ii)
$\Rightarrow T_{1} = 372 K = 99^{0} C and T_{2} = 310 K = 37^{0} C$

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