A copper calorimeter can with mass 0650 kg contains 0190 kg

A copper calorimeter can with mass 0.650 kg contains 0.190 kg of water and 0.019 kg of ice in thermal equilibrium at atmospheric pressure.

A) What is the temperature of the ice–water mixture?

B) If 0.750 kg of lead at a temperature of 255 C is dropped into the can, what is the final temperature of the system? (Assume no heat is lost to the surroundings.)

Solution

Given

Mass of copper m1 = 0.650kg

Specific heat capacity of copper c1 = 390 J/kg k

Mass of water m2 = 0.190 kg

Specific heat capacity of water c2 = 4190 kg

Mass of ice m3 = 0.019 kg

Mass of lead m4 = 0.725

Temperature of lead Ti = 255°c

Specific heat capacity of lead c3 = 130 J/kg k

Latent heat of fusion L = 334*10^3 J/kg

[130*0.725*(255-Tf)]=[390*.650*(Tf-0)]+[0.019*334*10^3]+[4190*(0.019+0.190)*(Tf-0)]

94.25(255-Tf) = 253.5Tf + 6346 + 875.71Tf

24033.75 - 94.25Tf = 1129.21Tf + 6346

1034.96 Tf = 17687.75

Tf = 17.09 °c