A 50g ice cube is added to 110g of water in a 62g aluminum cup. The water and cup initially have a temperature of 23°C. Find the initial temperature of the ice cube such that all of the water is just turned to ice. Use the following specific heats: water = 4186 J/(kg•K), ice = 2090 J/(kg•K), and aluminum = 900 J/(kg•K). The latent heat of fusion for water is 33.5e4 J/kg

Question

A 50g ice cube is added to 110g of water in a 62g aluminum cup.  The water and cup initially have a temperature of 23°C.  Find the initial temperature of the ice cube such that all of the water is just turned to ice.  Use the following specific heats: water = 4186 J/(kg•K), ice = 2090 J/(kg•K), and aluminum = 900 J/(kg•K).  The latent heat of fusion for water is 33.5e4 J/kg

bobpursley · Answer

find the heat needed...

Heatneeded=masswater*c(0-23)-masswater*Lf+massAl*Cal*(0-23)
Notice this heat is "negative), meaning it was lost. (it is negative heat gained).

now, the heat the ice gained.

massice*Cice*(0-Ti)

Now add the heats gained...set to zero.

heat ice gained+heat water(and aluminum) gaied [remember this is negative] =0
solve for Ti

tanmay bhoite · Answer

97.93 celcius