asked 218k views
5 votes
An object has been heated to 200

degrees Celsius. After 5 minutes it
has cooled to 131 degrees. The
ambient temperature is 20 degrees.
Rounded to the nearest tenth, what
will the temperature of the object be
at the end of 9 minutes?
[?] degrees Celsius

asked
User Tavia
by
8.5k points

1 Answer

4 votes

We can use Newton's law of cooling to solve this problem:

T(t) = T_a + (T_0 - T_a) * e^(-kt)

where T(t) is the temperature of the object at time t, T_a is the ambient temperature, T_0 is the initial temperature of the object, and k is a constant. We can solve for k by using the information that the object cools from 200 degrees to 131 degrees in 5 minutes:

131 = 20 + (200 - 20) * e^(-5k)

Simplifying this equation, we get:

e^(-5k) = 0.625

Taking the natural logarithm of both sides, we get:

-5k = ln(0.625)

k = -ln(0.625) / 5

k ≈ 0.1078

Now we can use this value of k to find the temperature of the object after 9 minutes:

T(9) = 20 + (200 - 20) * e^(-0.1078 * 9)

T(9) ≈ 94.9 degrees Celsius

Therefore, the temperature of the object at the end of 9 minutes will be approximately 94.9 degrees Celsius.

answered
User Abhisekp
by
7.9k points
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