A calorimeter consists of a massless beaker that contains 20.0 grams of solid water (i.e., ice) at −20 °C.?
A calorimeter consists of a massless beaker that contains 20.0 grams of solid water (i.e., ice) at −20 °C. Then 800 grams of lead at 80.0 °C are added to the calorimeter. a) Find the final temperature of the calorimeter after equilibrium is reached. b) What fraction of the ice is melted? [The specific heat of lead is 130 J kg ⋅ C°. ]
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Let's assume that all the ice melts and that the final temperature of the water is T. If we get a negative number, then we'll know that assumption was wrong.
latent heat of fusion of water = 334 kJ/kg
specific heat of ice = 2000 J/kg·ºC
(the value actually varies by temperature -- I'll use the value for -10ºC)
heat given up by ice/water = heat lost by lead
0.0200kg * (2000J/kg·ºC * 20ºC + 334000J/kg + 4186J/kg·ºC * T)
... = 0.800kg * 130J/kg·ºC * (80.0ºC - T)
7480J + 83.72J/ºC * T = 8320J - 104J/ºC * T
188J/ºC * T = 840 J
T = 4.47ºC ◄
Hope this helps!