A cup of coffee has cooled from 98degreesC to 50degreesC after 15 minutes in a room at 25degreesC. How long will it take to cool to 40degreesC?
Someone else helped me on a problem similar to this, however I keep getting it wrong by decimals. i.e the answer is 35.987 but i put in 35.867
I can't imagine why I'm getting it wrong, ive checked and double checked my formulas over and over
Thank you
https://www.jiskha.com/questions/1776107/A-cup-of-coffee-has-cooled-from-95degreesC-to-60degreesC-after-13-minutes-in-a-room
Too bad you didn't show your work...
25+(98-25)e^(-15k) = 50
k = 0.0714
So, to find t when T=40,
25+73e^(-0.0714t) = 40
Is this what you did?
If not, what did you do?
To determine how long it will take for the coffee to cool to 40 degrees Celsius, you can use Newton's Law of Cooling. This law states that the rate of temperature change of an object is directly proportional to the temperature difference between the object and its surroundings.
First, let's calculate the initial temperature difference between the coffee and the room. The initial temperature difference is given by:
ΔT_initial = Initial temperature of the coffee - Room temperature
ΔT_initial = 98°C - 25°C
ΔT_initial = 73°C
Similarly, let's calculate the final temperature difference between the coffee and the room. The final temperature difference is given by:
ΔT_final = Final temperature of the coffee - Room temperature
ΔT_final = 40°C - 25°C
ΔT_final = 15°C
Now, we can set up a proportion using these two temperature differences. The proportion will be:
(Rate of change of temperature)/ΔT_initial = (Rate of change of temperature at the final temperature)/ΔT_final
The rate of change of temperature is the reciprocal of the time taken to cool. Let's represent the time taken to cool to 40°C as t.
(1/t)/(73) = (1/15)/(15)
Simplifying this proportion, we get:
(1/t) = (73/15)
Now, let's solve this equation to find t, the time taken to cool to 40°C.
(1/t) = (73/15)
To isolate t, we can cross-multiply:
73t = 15
Dividing both sides of the equation by 73, we have:
t = 15/73
Now, let's calculate this value:
t = 0.205 (rounded to three decimal places)
Therefore, it will take approximately 0.205 hours, or 12.3 minutes, for the coffee to cool to 40 degrees Celsius.
Regarding your issue with decimals, it's important to be precise with your calculations while rounding to the required number of decimal places. Double-checking your formulas and using appropriate rounding methods (such as rounding up when the next digit is 5 or greater) should help in arriving at the correct answer.