Your team has been called in to solve a problem encountered by a fast food restaurant. They believe that their coffee should be brewed at 170 deg Fahrenheit. However, at temperature it is too hot to drink, and a customer who accidentally spills the coffee on himself might receive third degree burns.
What they need is a special container that will heat the water to 170 deg, brew the coffee at that temperature, then cool it quickly to a drinkable temperature, say 140 deg F and hold it there, or at least keep it at or above 120 deg F for a reasonable period of time without further cooking. Yo cool down the coffee, 3 companies have submitted proposals with these specifications.
a)the Centikeeper Company has a container that will reduce the temperature of a liquid from 200 deg F to 100 deg F in 90mins by maintaining a constant temperature of 70deg F
B)The TempControl Company has a container that will reduce the temperature of a liquid from 200deg F to 110deg F in 60mins by maintaining a constant temperature of 60deg F.
C)the hot n cold Inc. has a container that will reduce the temperature of a liquid from 210deg F to 90deg F in 30mins by maintaining a constant temperature of 50deg F.
Your job is to make a recommendation as to which container to purchase . For this you will need Newton's Law of Cooling, whick follows:
u(t)=T+(u base 0 - T)e^kt k<0
In this formula,
T represents the temperature of the surrounding medium
u base 0 is the initial temperature of the heated object
t is the length of time in minutes
k is a negative constant
u represents the temperature at time t
1)Use Newtons's law of cooling to find the constant k of the formula for each container
2)Use a graphing utility to graph each relation.
3)How long does it take each container to lower the coffee temperature from 170deg F to 140deg F
4)How long will the coffee temperature remain between 120deg F and 140deg F
5)On the basis of this information, whick company should get the contract with McNewton's? What are your reasons?
6)Define "capital cost" and "operating cost". How might they affect your choice?
April 20th 2009, 10:20 AM
There are many archived discussions available, such as this one. (Wink)