, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the water cools from 90°C to 85°C in 1 minute at a room temperature of 30°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
Stanton D. answered • 05/02/20
Tutor to Pique Your Sciences Interest
Hi Arianna P.,
You can certainly integrate the T' = -kT , where T is redefined as the temperature in C above 30C; that would be -ke^-kT + C, plug in the 1st minute observations and solve for k, then set into the equation. Or, you could estimate, based on 4 1-minute intervals, as follows T: first minute, delta T = -5C, from an initial T=60C; 2nd minute, delta T = -4.6C, based on ratioing from first minute and initial T = 55C; 3rd minute, delta T = -4.2C based on ratioing from first minute and approximate initial T of 50C; and 4th minute, delta T = -3.8C based on ratioing from first minute and approximate initial T = 46C. That's delta T = -17.6 or 72C absolute. Done in about 1 minute (negligible additional cooling of the coffee!)
-- Cheers, -- Mr. d.
