A bucket of water with a mass of 20 kg at 18°C is to be cooled to 0°C by dropping ice cubes at 0°C into it. The latent heat of fusion of ice is 334 kJ/kg, and the specific heat of water is 4.18 kJ/kg.°C. The amount of ice that needs to be added is
A)4.5 kg
B)0.25 kg
C)10 kg
D)20 kg
E)8.6 kg

Question

Quizplus · Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
C=4.18 "kJ/kg.K"
h_melting=334 "kJ/kg.K"
m_w=20 "kg"
T1=18 "C"
T2=0 "C"
DELTAT=T2-T1 "C"
"Noting that there is no energy transfer with the surroundings and the latent heat of melting of ice is 
transferred form the water, and applying energy balance E_in-E_out=dE_system to ice+water gives"
dE_ice+dE_w=0
dE_ice=m_ice*h_melting
dE_w=m_w*C*DELTAT "kJ"
 
"Some Wrong Solutions with Common Mistakes:"
W1_mice*h_melting*(T1-T2)+m_w*C*DELTAT=0 "Multiplying h_latent by temperature difference"
W2_mice=m_w "taking mass of water to be equal to the mass of ice"

A Bucket of Water with a Mass of 20 Kg