Question

Suppose a small metal object, initially at a temperature of 50 degrees, is immersed in a room which is held at the constant temperature of 90 degrees. It takes 1 minutes for the temperature of the object to reach 70 degrees. Calculate the heat transfer coefficient r , i.e. the constant of proportionality in the differential equation that describes Newton's law of cooling.

Answer 1

In this problem, we use Newton's Law of Cooling to calculate the heat transfer coefficient (r).

Step-by-step explanation:

In this problem, we can use Newton's Law of Cooling to calculate the heat transfer coefficient (r).

Newton's Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature. Mathematically, it can be represented as:

dT/dt = -r(T - Ts)

Where dT/dt is the rate of change of temperature, r is the heat transfer coefficient, T is the temperature of the object, and Ts is the temperature of the surrounding.

We are given that the temperature of the object initially is 50 degrees and it takes 1 minute for the temperature to reach 70 degrees.

Using this information, we can substitute the given values into the differential equation and solve for r:

70 - 50 = -r(70 - 90)

-20 = -r(-20)

r = 1

Therefore, the heat transfer coefficient, r, is 1.

Answer 2

Step-by-step explanation:

Solution is attach below