Final answer:
Newton's Law of Cooling states that the rate of cooling of an object is directly proportional to the difference in temperature between the object and its surroundings. To solve the given problem, substitute the known values into Newton's Law of Cooling equation and solve for the temperature of the water after 20 minutes.
Step-by-step explanation:
Newton's Law of Cooling:
Newton's Law of Cooling states that the rate of cooling of an object is directly proportional to the difference in temperature between the object and its surroundings. Mathematically, it can be represented as:
T(t) = T_s + (T_i - T_s) * e^(-kt),
where T(t) is the temperature of the object at time t, T_i is the initial temperature of the object, T_s is the temperature of the surroundings, k is the cooling constant, and e is the base of the natural logarithm. This law is used to analyze the cooling or heating of objects in various situations.
Solving the given problem:
In the given problem, the initial temperature of the water is 100°C, the surrounding temperature is 25°C, and it cools in 10 minutes to 88°C. To find the temperature of the water after 20 minutes, we substitute the known values into Newton's Law of Cooling equation:
T(20) = 25 + (100 - 25) * e^(-k * 20),
Solving the equation using the given information, we can find the value of k. Once we have the value of k, we can substitute it into the equation to find the temperature of the water after 20 minutes.