# 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...

See full answer below.

#### Learn more about this topic: Types of Heating & Cooling Systems

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Chapter 10 / Lesson 9
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You can choose from a number of different heating and cooling systems to make your home comfortable to live in. Watch this video to learn about the advantages and disadvantages of forced air, radiant heat, baseboard heat and geothermal systems.