Question

A black rectangular surface of area A emits energy E per second at 27°C. If length and breadth is reduced to `(1/3)^("rd")` of initial value and temperature is raised to 327°C then energy emitted per second becomes ______.

Options

• `(4"E")/9`

• `"E"/9`

• `(16"E")/9`

• `(2"E")/9`

Answer 1

A black rectangular surface of area A emits energy E per second at 27°C. If length and breadth is reduced to `(1/3)^("rd")` of initial value and temperature is raised to 327°C then energy emitted per second becomes `underlinebb((16"E")/9)`.

Explanation:

E = `sigma "AT"^4`

`therefore "E"_2/"E"_1 = "A"_2/"A"_1.("T"_2/"T"_1)^4`

`"A"_2 = "A"_1/9`  `therefore "A"_2/"A"_1 = 1/9`

`"T"_1` = 27 + 273 = 300 k

`"T"_2` = 327 + 273 = 600 k

`therefore "T"_2/"T"_1 = 600/300` = 2 

`therefore "E"_2/"E"_1 = 1/9 xx (2)^4 = 16/9`

`therefore "E"_2 = 16/9 "E"_1 = 16/9` E