A heated object (at time `t=0` and temperature `T=T_(0))` is taken out of the oven to cool and placed on a table near an open window Write an expression for its temperature as function of time `T` where `T_(s)` is the surrounding temperature .

Options

A. `T=T_(s)-(T_(0)+T_(s))e^(-kt)`
B. `T=T_(s)+(T_(0)+T_(s))e^(-kt)`
C. `T=T_(s)+(T_(0)-T_(s))e^(-kt)`
D. `T=T_(s)-(T_(0)-T_(s))e^(-kt)`

Answer

C

Explanation

`(d theta)/(dt) =-K (T -T_(s))`
`underset(T_(0))overset(T)int(d theta)/(T -T_(s)) = -K underset(0)overset(t)intdt log ((T-T_(s))/(T_(0)-T_(s)))=-Kt+C` .