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A solid at temperature T(1) is kept in a...

A solid at temperature `T_(1)` is kept in an evacuated chamber at temperature `T_(2)gtT_(1)` . The rate of increase of temperature of the body is proportional to

A

`t_(2)^(4) - t_(1)^(4)`

B

`(t_(2)^(4) +273 ) - (t_(1)^(4) +273 )`

C

`t_(2) -t_1`

D

`t_(2)^(2) :t_(1)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Rate of heat radiation emitted by a body at temperature `T_(1)^@ C (=(t_1 + 273 ) K)`
`u_1 = e sigma A ( T_1 +273 )^4 `
Rate of heat radiation absorbed by a body due to surrounding temperature `T_(2)^@ C ( (T_2 + 273 ) K) , u = e sigma A (t_2 + 273 )^4`
Net rate of heat absorbed by the body
`=u -u_1 = e sigma A[(t_2 + 273 )^4 - (t_1 + 273 )^4]`
None of the given options is correct
option (a) would be correct if ` t_1 and t_2 ` were in kelvin
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