A container of hot liquid is placed in a freezer that is kept at a constant temperature of . The initial temperature of the liquid is . After 3 minutes, the liquid's temperature is . How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places.
A) 1.89 minutes
B) 2.84 minutes
C) 3.16 minutes
D) 1.26 minutes
E) 3.47 minutes

Question

A container of hot liquid is placed in a freezer that is kept at a constant temperature of  . The initial temperature of the liquid is  . After 3 minutes, the liquid's temperature is  . How much longer will it take for its temperature to decrease to  ? Round your answer to two decimal places.
A) 1.89 minutes 
B) 2.84 minutes 
C) 3.16 minutes 
D) 1.26 minutes 
E) 3.47 minutes

Quizplus · Accepted Answer

Using the formula for Newton's law of cooling, we have:

T(t) = T_f + (T_0 - T_f)e^(-kt)

Where:
T(t) = temperature at time t
T_f = freezer temperature = 11°C
T_0 = initial temperature of liquid = 80°C (converted from Kelvin to Celsius)
k = cooling constant
t = time

Using the given data, we can find k:

18 = 11 + (80 - 11)e^(-k*3)
e^(-3k) = 0.2225
-k = ln(0.2225/-1)
k = 0.474

Now we can use the formula to find the time it takes for the temperature to decrease to 79°C:

79 = 11 + (80 - 11)e^(-0.474t)
e^(-0.474t) = 0.98875
t = ln(1/0.98875)/0.474

t ≈ 3.16 minutes, rounded to two decimal places.

Therefore, the best choice is C - 3.16 minutes.

A Container of Hot Liquid Is Placed in a Freezer