Question 28509: a skillet is removed from an oven whose temperature is 450 degrees and is placed in a room whose temperature is 70 degrees. after 5 minutes, the temperature of the skillet is 400 degrees. how long will it be until it's temperature is 150 degrees?
Found 2 solutions by wuwei96815, bmauger:
Answer by wuwei96815(245)   (Show Source):
You can put this solution on YOUR website! The skillet is losing 450-400/5 or 10 degrees per minute. I am assuming that the loss in heat is a linear function.
Let x = the number of minutes needed to reach 150 degrees.
x = 450-150/10 = 300/10 = 30 minutes
I hope that my reasoning was correct.
Answer by bmauger(101) (Show Source):
You can put this solution on YOUR website! I read this problem and assumed it wasn't a linear problem since you gave a room temperature and that instead that this is a half-life/physics problem... Otherwise what would be the purpose of telling us the room is 70 degrees? And if it is a linear problem, and the skillet is loosing 50 degrees every 5 minutes, then in an hour the skillet will have lost 600 degrees and will be -150 degrees, which doesn't make much sense. Though in the future, you should probably explain what you're studying when you give the problem.
What we want to look at is the rate at which the temperature is approaching 70 degrees. Because 70 degrees really isn't measuring anything, except for the baseline temperature of the room, I would rewrite our temperatures as if the baseline 70 degrees was 0. In other words:
A skillet is removed from an oven whose temperature is 450-70=380 degrees and is placed in a room whose temperature is 70-70=0 degrees. after 5 minutes, the temperature of the skillet is 400-70=330 degrees. how long will it be until it's temperature is 150-70=80 degrees?
Now that we have our baseline at 0, it's much easier to write a decay equation in the form:
In this format we can find our decay rate (r) by putting in 5 minutes for time (t), 380 for our principle (P), and 330 for our total (T) and write:
 Taking the natural log of both sides:
Now we can rewrite our equation to find out what time (t) will be when our total (T) is 80.
 The fractions you can't read are 33/38 & t/5
 Natural log of both sides:
So your answer = 55 minutes and 13 seconds:
Graph:
Green = skillet temperature(time) minus 70 degrees
Red = 150-70=80 degrees
Intersect at time=55.22
|
|
|
