An igloo, a hemispherical enclosure built of ice $(1.67 J / m - s ° C)$ , has as inner radius of 2.50m. The thickness of the ice is 0.5m. At what rate must thermal energy be generated to maintain the air inside the igloo at $5 ° C$ when the outside temperature is - $40 ° C ?$ Ignore all thermal energy losses through the ground or by air currents.

Option 1 -

2.25 πkW

Option 2 -

4.5 πkW

Option 3 -

1.25 πkW

Option 4 -

5 πkW

2 Views | Posted 3 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 weeks ago

Correct Option - 1

Detailed Solution:

$\frac{d H}{d t} = - 2 π x^{2} k \frac{d T}{d x}$

$\frac{d H}{d t} = \frac{2 π \times k \times 45}{\frac{1}{2.5} - \frac{1}{3}} = 2.25 π k W$

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