. A 0.30 kg coffee mug is made from a material that has a specific heat capacity

Question

. A 0.30 kg coffee mug is made from a material that has a specific heat capacity of 990 J/(kg. C) and contains 0.31 kg of water. The cup and water are at 25 °C. To make a cup of coffee, a small electric heater is immersed in the water and brings it to a boil in two minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.(cw 4186 J/kg.oC) 8. A cube of aluminum 25.0 cm on each side is cooled from 126 °C to 20 °C. If the energy removed from the aluminum cube were added to a copper cube of the same size at 30 °C, what would be the final temperature of the copper cube?(PAI 2700 kg/m*; Pcopper 8 oC

Explanation / Answer

7)

Total energy needed is
E = 990 J/(kg·°C) x 0.3 kg x 75C + 4186 J/kgC x 0.31 x 75
E = 22275 J + 97324.5 J = 119599.5 J = 119.6 kJ

power = 119599.5 J / 120s = 996.7 W

8)

heat yielded by Al = heat gained by Cu
(m*c*?T)_Al = (m*c*?T)_Cu

Al:
mass m = ?V = 2700kg/m³ * (0.250m)³ = 42.2 kg
?T = 106ºC

Cu:
mass m = 8890kg/m³ * (0.25m)³ = 138.9 kg
?T = ?

so
42.2kg * cAl * 106ºC = 138.9kg * cCu * ?T
?T = 32.2ºC * cAl / cCu

So, as you might expect, the change in temperature depends on what you take as the values for cAl and cCu (the specific heats of aluminum and copper, respectively). For
cAl = 910 J/kg·ºC
cCu = 390 J/kg·ºC,
I get
?T = 32.2º * 910/390 = 75.1ºC
and so the final temperature of the copper is
T = 30ºC + 75.1ºC = 105.1ºC ?

Hope this helps!

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