SATHEE: Heat and Thermodynamics 3 Question 32

Heat and Thermodynamics 3 Question 32

32. A point source of heat of power $P$ is placed at the centre of a spherical shell of mean radius $R$ . The material of the shell has thermal conductivity $K$ . If the temperature difference between the outer and inner surface of the shell is not to exceed $T$ , the thickness of the shell should not be less than …… .

(1991, 1M)

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Solution:

Thermal resistance $= \frac{l}{K A} = \frac{t}{K (4 π R^{2})} (t =$ thickness $)$ Now, rate of heat transfer $= \frac{Temperature difference}{Thermal resistance}$

$= \frac{T}{t / 4 π K R^{2}} = \frac{4 π K T R^{2}}{t}$

Equating this rate with the power of the source.

$∴ P = \frac{4 π K T R^{2}}{t}$ or $t = \frac{4 π K T R^{2}}{P}$

or thickness $t$ should not exceed $\frac{4 π K T R^{2}}{P}$ .

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Heat and Thermodynamics 3 Question 32

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