Select the correct answer. The formula below, Newton's law of cooling, allows us to calculate the temperature of an object as it cools. T = R + (T0 - R) e-kt T = temperature of the object after t minutes T0 = initial temperature R = temperature of the surroundings k = cooling rate (depends on the object and conditions) Suppose the temperature in Denver, Colorado was 55°F when a 5°F arctic cold front moved over the state. Using k = 0.012, how long would it take a puddle of water to freeze? (Recall that water freezes at 32°F.) A. just over 51 minutes B. just over 55 minutes C. just over 61 minutes D. just over 65 minutes

Question

Physics

Dyer

6 June, 05:23

Select the correct answer. The formula below, Newton's law of cooling, allows us to calculate the temperature of an object as it cools. T = R + (T0 - R) e-kt T = temperature of the object after t minutes T0 = initial temperature R = temperature of the surroundings k = cooling rate (depends on the object and conditions) Suppose the temperature in Denver, Colorado was 55°F when a 5°F arctic cold front moved over the state. Using k = 0.012, how long would it take a puddle of water to freeze? (Recall that water freezes at 32°F.) A. just over 51 minutes B. just over 55 minutes C. just over 61 minutes D. just over 65 minutes

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Silky · Answer 1

Option A is correct.

The water freezes in just over 51 minutes

Explanation:

T = R + (T₀ - R) e-ᵏᵗ

T = temperature of the object after t minutes = 32°F

T₀ = initial temperature = 55°F

R = temperature of the surroundings = 5°F

k = cooling rate (depends on the object and conditions) = 0.012

32 = 5 + (55 - 5) e-ᵏᵗ

32 - 5 = 50 e-ᵏᵗ

27/50 = e-ᵏᵗ

e-ᵏᵗ = 0.54

-kt = In 0.54 = - 0.6162

0.012 t = 0.6162

t = 51.3 minutes.