Answered: Define Cooling and Heating in relation…

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Question

Define Cooling and Heating in relation with calculus?

Expert Solution

Step 1

Solution:

The rate of heating or cooling of an object is directly proportional to the temperature between the object and surrounding. Let T be the temperature of the object and T_s be the temperature of the surrounding.

Step 2

Integrating on both side

Taking exponential on both sides

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Similar questions

The figure below, called a heating curve, represents the temperature of a block of ice as thermal energy is added. (The ice melts into water and then vaporizes into steam.) The thermal energy required to change phase from solid to liquid is calculated using the equation Q = mLf, where Lf is called the (latent) heat of fusion. The thermal energy required to change phase from liquid to gas is calculated using the equation Q = mLv, where Lv is called the (latent) heat of vaporization. cice = 2100 J/kg·K; cwater = 4186 J/kg·K; csteam = 2000 J/kg·K; Lf of water = 3.33 x 105 J/kg; Lv of water = 2.26 x 106 J/kgA snowball made of ice at -11.2 degrees Celsius is thrown at a brick wall. Assuming no energy is lost to the wall or surrounding air, how fast would the snowball have to be thrown in order to completely vaporize upon impact? Include units in your answer. More information. REFER TO THE IMAGE FOR CLEARER DIRECTIONS