Question

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Newton's law of cooling states that the tempreture of an object changes at a rate proportional to the difference between the temperature of the object itself and the temprature of its surroundings ( the ambient air temperature in most cases ).
suppose that the ambient tempreture is \(75ْ F\) and that the rate constant is
\(0.05 (\text{min})^{-1}\) .
*write a defferential equation for the temperature of the object at any time.

Answer 1

**Note that the differential equation is the same wether the temperature of the object is above or below the ambient temperature

Answer 2

@LastDayWork @Mashy @terenzreignz @SithsAndGiggles @ganeshie8 @Luigi0210
@HARSH123 @Zale101 @zepdrix

Answer 3

\[\frac{ dt }{ T _{t}-T _{s} } = k \int\limits_{t _{1}}^{t _{2}}dt\]

Answer 4

Just substitute 75 deg F to Ts and 0.05(min)^-1 to k

Answer 5

and thats all ?

Answer 6

Yeah.

Answer 7

thank you !