First slide

Conduction

Question

Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio 2:3. The outer surface of one plate is maintained at 10°C and that of the other at 0 DC. What is the temperature at the common surface?

Difficult

A

0⁰C
B

2.5⁰C
C

5⁰C
D

6.5⁰C

Solution

If T is the temperature of the interface .of two plates of same area, then
$\frac{d Q}{d t} = \frac{K_{1} A (10 - T)}{Δ x_{1}} = \frac{K_{2} A (T - 0)}{Δ x_{2}}$
or $\frac{K_{1} A (10 - T)}{Δ x_{1}} = \frac{\frac{3}{2} K_{1} A (T - 0)}{3 / 2 Δ x_{1}} (∵ \frac{K_{1}}{K_{2}} = \frac{2}{3} and \frac{Δ x_{1}}{Δ x_{2}} = \frac{2}{3})$
or $10 - T = T - 0 or T + T = 10 or 2 T = 10$
$∴ T = 5^{\circ} C$

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