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deff fn [24]
3 years ago
8

A calculator is required to obtain the final answer on this question. A solid metal sphere at room temperature 20oC is dropped i

nto a container of boiling water (100oC). If the temperature of the sphere increases 15o in 9 seconds, find the temperature of the ball after 18 seconds in the boiling water. (Assume the sphere obeys Newton's Law of Cooling.)
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
5 0

Answer:

T = 47.1875°C

Step-by-step explanation:

Given:

Surrounding temp, Ts = 100°C

Initial Temperature ,T0= 20°C

Increase in temperature = 15°C

Final temperature, T = 20 + 15 = 35°C

Time, t = 9 seconds

Let's take Newton's law of cooling:

T - Ts = (T_0 - Ts)e^k^t

We'll solve for k

35 - 100 = (20 - 100)e^9^k

-65 = (-80)e^9^k

Divide both sides by -5

13 = (16)e^9^k

9k = ln (\frac{13}{16})

k = \frac{1}{9} ln (\frac{13}{16})

k = -0.02307104053

Let's now find the temperature of the ball after 18 seconds in boiling water.

Use the Newton's equation again:

T - Ts = (T_0 - Ts)e^k^t

T - 100 = (20 - 100)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8

T - 100 = (-80)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8

T - 100= -52.8125

T = 100 - 52.8125

T = 47.1875°C

Temperature of the ball after 18 seconds in boiling water is 47.1875°C

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