Question

Sienna's mom is making her an egg salad. Using an instant-read thermometer, her mom takes the hard-boiled egg when it is 205°F and places it in 61°F water to cool. Four minutes later, the temperature of the egg is 113°F. Apply Newton's Law of Cooling to determine the cooling rate.

A. True

B. False

Answer 1

According to Newton's Law of Cooling, the cooling rate of the hard-boiled egg can be determined by applying the formula T = T0 + (T1 - T0)e^(-kt), where T is the temperature at a given time, T0 is the initial temperature, T1 is the final temperature, k is the cooling constant, and t is the time elapsed. By plugging in the given values, we can solve for k and determine the cooling rate.

Step-by-step explanation:

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. In this case, we can apply this law to determine the cooling rate of the hard-boiled egg.

The initial temperature of the egg is 205°F and the final temperature is 113°F after four minutes. We can use the formula for Newton's Law of Cooling:

T = T0 + (T1 - T0)e^(-kt)

Where T is the temperature at a given time, T0 is the initial temperature, T1 is the final temperature, k is the cooling constant, and t is the time elapsed. By plugging in the given values, we can solve for k:

113 = 205 + (113 - 205)e^(-4k)

After solving for k, we can determine the cooling rate.