First slide

Conduction

Question

The two ends of a metal rod are maintained at temperatures 100°C and 110° C. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200°C and 210°C, the rate of heat flow will be

Very Easy

A

8.0 J/s
B

4.0 J/s
C

44.0 J/s
D

16.8 J/s

Solution

Rate of heat flow through a rod is given by
$\frac{d Q}{d t} = - K A \frac{d T}{d x}$
$Let length of the rod be L .$
$Case I : \frac{d T}{d x} = \frac{Δ T}{Δ x} = \frac{110 - 100}{L} = \frac{10}{L}$
$∴ \frac{d Q_{1}}{d t} = - K A \frac{10}{L}$ . . . .(i)
$Also, \frac{d Q_{1}}{d t} = 4 J s^{- 1}$ . . . .(ii)
$Case II : \frac{d T}{d x} = \frac{Δ T}{Δ x} = \frac{210 - 200}{L} = \frac{10}{L}$
$∴ \frac{d Q_{2}}{d t} = - K A \frac{10}{L}$ . . . .(iii)
$So, from equations (i), (ii) and (iii)$
$\frac{d Q_{2}}{d t} = \frac{d Q_{1}}{d t} = 4 J s^{- 1}$

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