This problem concerns the cooling of water in a well-insulated, cylindrical cup

Question

This problem concerns the cooling of water in a well-insulated, cylindrical cup that is opened at the top.

0.436 kg of water at 87 0C is poured into the cup which is left to stand on a table at an ambient temperature of 25 0C. The specific heat capacity of water is 4150 J kg-1K-1 and the U-value is 9.93 Wm-2K-1. The area of the water surface that is exposed to the surrounding air is 0.00441 m2.

Calculate the time taken, in seconds, for the water in the cup to cool to a drinkable temperature of 54 0C, giving your answer to the nearest integer. Show working.

Explanation / Answer

(T?To)=(T1?To)e^(?kt)

here, T= 54 C ; T1 = 87 C; T0 = 25 C

k = (U-value)(Surface Area)/(mass)(Heat Capacity) = (9.93*0.00441)/(0.436 *4150) = 0.000024202

substitute in above equation,

(54-25) = (87-25)*e^(-0.000024202*t)

t = 31395.6927 sec.

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