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A body with an initial temperature theta...

A body with an initial temperature `theta_(1)` is allowed to cool in a surrounding which is at a constant temperature of `theta_(0) (theta lt theta_(1))` Assume that Newton's law of cooling is obeyed Let `k =` constant The temperature of the body after time t is best experssed by .

A

`(theta_(1)-theta_(0))e^(-kt)`

B

`(theta_(1)-theta_(0))"In"(kt)`

C

`theta_(0)+(theta_(1)-theta_(0))e^(-kt)`

D

`theta_(1)e^(-kt)=theta_(0)`

Text Solution

Verified by Experts

`(d theta)/(dt)=-k (theta-theta_(0))`
`int_(theta_(1))^(theta)( d theta)/(theta -theta_(0))=-k int_(0)^(1)dt = theta =theta_(0)+(theta_(1)-theta_(0))e^(-kt)`
Hence c is correct.
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