A hot metal bar is submerged in a large reservoir of water whose temperature is 40 F. The...

Question:

A hot metal bar is submerged in a large reservoir of water whose temperature is 40 F. The temperature of the bar 20 sec after submersion is 90 F. After 1 min submerged, the temperature has cooled to 70 F.

(a) Determine the cooling constant k.

(b) What is the differential equation satisfied by the temperature F(t) of the bar? Use F for F(t).

(c) What is the formula for F(t)?

(d) Determine the temperature of the bar at the moment it is submerged.

Application of Newton's Law of Cooling:

Newton's Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the surroundings temperature.

{eq}\frac{dT}{dt} = - k(T - T_m) {/eq}

Where {eq}T_m {/eq} is the surroundings temperature and {eq}T {/eq} is the initial temperature of an object.

And its Solution is:

{eq}T(t) = T_m + ( T - T_m)e^{ -kt} {/eq}

Answer and Explanation:

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a.)

Accroding to the Newton's Law of Cooling we can write:

{eq}T(t) = 40 + ( T_1- 40 ) e^{-kt} {/eq}

Where, {eq}t {/eq} is the time measured in...

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