Final answer:
Using Newton's Law of Cooling and plugging in the given values of the absolute difference in temperature and the difference in time, we calculate and solve for K. This involves dividing the rate of change in temperature by the negative temperature difference to get the value of K rounded to 4 decimal places.
Step-by-step explanation:
Suppose that a cup of ice tea having a temperature of 2°F is placed in a study area at 32°F. One hour later the tea has a temperature of 13°F. To find the value of K, we need to apply Newton's Law of Cooling, which is defined as the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. So, the formula to find the value of K is: dT/dt = -K(T - Ts), where Ts is the surrounding temperature, T is the body temperature at time 't' and K is the constant we are trying to find. Substituting the given values into the equation, we have (13 - 2) / (1 hour) = -K(13 - 32). Solving for K, we get K = -((13 - 2) / (1 hour)) / (13 - 32). After solving, we round to 4 decimal places to get the value of K.
Learn more about Newton's Law of Cooling