Question

# Need to determine the model equation for the conservation of energy it should have 5 terms...

Need to determine the model equation for the conservation of energy it should have 5 terms then the equation need to be solve for L (latent heat of fusion of water: just the variable L) then the latent heat of fusion need to be calculated using the data given. Mcup=0.0593kg, Mcup+water=0.1984kg, Mwater=0.1391kg, Mice=0.0204kg, Initial temp of water and cup Tw,i=38.6 Celsius, Temp final of water,ice,cup=23.0 Celsius, Total mass cup,water,ice=0.2188kg. Temp of ice T ice,i 0 Celsius. Delta T water and cup 15.6 Celsius, Delta T for ice cube 23.0 Celsius, Delta T for ice cube water 23.0 Celsius. I’m not sure if i solved for the Delta right. Also is it possible that the ice could be colder then o degrees Celsius if the temperature inside the freezer is -23.4 Celsius. Please help

Mcup=0.0593kg

Mcup+water=0.1984kg,

Mwater=0.1391kg,

Mice=0.0204kg

Initial temp of water (Tw) = 38.6 C

Initial temp of ice (Ti) = - 23.4 C

Final temp = 23 C

Specific heat of water = 1 cal/kg/C

Specific heat of ice = 0.5 cal/kg/C

L= ?

Specific heat of cup be = S

Heat gained by ice at – 23.4 C to ice at 0 C = Mice * 0.5 * 23.4

Heat gained by ice at 0 C to water at 0 C = Mice * L

Heat gained by water at 0 C to water at 23 C = Mice * 1 * 23

Heat lost by water at 38.6 C to water at 23 C = Mwater * 1 * (38.6 – 23 )

Heat lost by cup at 38.6 C to cup at 23 C = Mcup * S * (38.6 – 23 )

Heat gained = Heat Lost

Mice * 0.5 * 23.4 + Mice * L + Mice * 1 * 23 = Mwater * 1 * (38.6 – 23 ) + Mcup * S * (38.6 – 23 )

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