00:01
Okay, this question asks, a bottle of water with temperature 70 degrees fahrenheit is placed into a refrigerator with an internal temperature of 34 degrees fahrenheit.
00:10
And after 20 minutes, the temperature of the water has decreased to 52 degrees fahrenheit.
00:15
In part a, asked to give the cooling constant k rounded to six decimal places.
00:20
This problem can be solved using the newton's law of cooling equation, which is t of time t, equals t .s, which is the surrounding, constant temperature plus t not t of zero which is the initial temperature minus t s times e to the negative k times the little t the little t here is time and the k is what we're trying to solve for here so let's rearrange this equation so that um we can solve for k so doing t of t minus t s divided by t0 minus t s equals e negative k times t if we raise this to the natural log l n of t of t minus t divided by t o minus t s equals negative k times t so simply doing dividing each side by negative will have k equals negative that should be a negative sorry negative t so one over t times l -n of t of t minus t s over t o minus ts and once we have this formula here we can go ahead and plug in our values we're given that the bottle of water has a 70 degree fahrenheit so that would be t o equals 70 degree fahrenheit and is placed into a constant surrounding temperature of 34 degrees when it's put into the refrigerator.
02:03
T .s.
02:04
Is 34 degrees.
02:05
And the time it took for the water of the temperature of the water to decrease was 20 minutes, and t of 20 was 52 degrees fahrenheit.
02:16
So solving for k was 1 over 20, ln of t of 20, which is 52 minus 34, over 70 minus.
02:25
34.
02:26
I'll quickly do that in my calculator real quick.
02:29
Negative 1 over 20 times ln or the natural log 52 minus 34 divided by 70 minus 34 equals k equals to the six.
02:40
We used to round to the six decimal places so 0 .03, 4, 6, 5, 7.
02:47
1, 2, 3, 4, 5, 6.
02:49
6.
02:49
Okay.
02:50
Okay.
02:51
If you wanted to add more, there would be four because it just continues on to three, five, nine...