b) At the Cafe at the end of the pier Captain Barbossa ordered a Cup of coffee, the cooling of which follows the following Differential equation dT -k (T – E) dt Where T is temperature of the coffee and E is the temperature of the environment . Temperature is measured in degrees Celsius and the timet is in minutes. The environment temperature is a cool 16°C (i) The coffee at 92°C was left to stand on the table for 3 minutes after which it had cooled to 72°C, Derive a solution to this differential equation and calculate the value of k Correct to 4 decimal places. (ii) If Captain Barbossa can drink the coffee at 55°C, how Long does he have to wait? (Correct to the nearest minute)
b) At the Cafe at the end of the pier Captain Barbossa ordered a Cup of coffee, the cooling of which follows the following Differential equation dT -k (T – E) dt Where T is temperature of the coffee and E is the temperature of the environment . Temperature is measured in degrees Celsius and the timet is in minutes. The environment temperature is a cool 16°C (i) The coffee at 92°C was left to stand on the table for 3 minutes after which it had cooled to 72°C, Derive a solution to this differential equation and calculate the value of k Correct to 4 decimal places. (ii) If Captain Barbossa can drink the coffee at 55°C, how Long does he have to wait? (Correct to the nearest minute)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:b) At the Cafe at the end of the pier Captain Barbossa ordered a
Cup of coffee, the cooling of which follows the following
Differential equation
dT
-k (T – E)
dt
Where T is temperature of the coffee and E is the temperature
of the environment . Temperature is measured in degrees Celsius
and the timet is in minutes. The environment temperature
is a cool 16°C
(i)
The coffee at 92°C was left to stand on the table
for 3 minutes after which it had cooled to 72°C,
Derive a solution to this differential equation and
calculate the value of k Correct to 4 decimal places.
If Captain Barbossa can drink the coffee at 55°C, how
Long does he have to wait?
(Correct to the nearest minute)
(ii)
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