Question

Suppose a small metal object, initially at a temperature of 40 degrees, is immersed in a room which is held at the constant temperature of 70 degrees. It takes 2 minutes for the temperature of the object to reach 55 degrees.

Required:
a. Calculate the heat transfer coefficient r , i.e. the constant of proportionality in the differential equation that describes Newton's law of cooling.
r =_________

b. Suppose now that the room temperature begins to vary; i.e. Troom(t) = 90 + sin(0.1 t) . Use Newton's law of cooling and the heat transfer coefficient you calculated in the previous step to compute the temperature of the object as a function of time. Suppose that T(0) = 70 . T(t)

Answer 1

Answer:

1

Explanation:

Answer 2

a)The heat transfer coefficient  will be 0.231 .The concept of the Newtons law of cooling is used in the given problem.

What is newtons law of colling?

The pace at which an item cools is proportional to the temperature differential between the object and its surroundings,

According to Newton's law of cooling. Simply explained, in a cold environment, a glass of hot water will cool down faster than in a hot room.

The given data in the problem is;

T₀ is the initial temperature= 40°

$\rm T_S$  is the constant temperature = 70°

T is the final temperature = 55°

From the given equation the Newtons law of cooling;

$\rm T=T_S+(T_0-T_S)e^{-kt} \\\\ 55=70+(40-70)e^{-3k} \\\\-30 e^{-3k}=-15\\\\ e^{-3k}= -\frac{1}{2} \\\\ ln e^[3k}=ln 2 \\\\ K=\frac{1}{3} ln2 \\\\ K=0.231$

Hence the heat transfer coefficient  will be 0.231 .

To learn more about the Newtons law of cooling refer to the link;

https://brainly.com/question/14643865