Question

How many kg of ice at 0°C must be added to 0.6kg of water at 100°C in an insulated 0.1kg copper container and its contents to 30°C? The specific heats of water and copper are 4.2 and 0.39 kJ/kgK, respectively; the heat of fusion of ice is 335 kJ/kg.

Answer 1

.389 kg of ice required

Step-by-step explanation:

The heat absorbed by melting the ice and warming it to 30 C

must be equal to the heat lost by cooling the existing water and the copper from 100 to 30 C

First, melt the ice (this occurs at a constant temperature)

x * 335 kj/kg and warm this water x * 4.2 kj/kg-k * 30 k

(x = kg of ice required)

then cool the copper and the .6 kg water from 100 to 30 C (70 degrees)

.1 kg * .39 * 70 K + .6kg * 4.2 kj/kg-K * 70 K

then equate the two amounts of heat

x ( 335 + 4.2 *30) = .1 * .39 * 70 + .6 * 4.2 * 70

solve for x = .389 kg