Question

# Please Show all work, thank you! A copper block with a mass of 400 grams is...

Please Show all work, thank you!

A copper block with a mass of 400 grams is cooled to 77 K by being immersed in liquid nitrogen. The block is then placed in a Styrofoam cup containing some water that is initially at +50.0°C. Assume no heat is transferred to the cup or the surroundings. The specific heat of liquid water is 4186 J/(kg °C), of solid water is 2060 J/(kg °C), and of copper is 385 J/(kg °C). The latent heat of fusion of water is 3.35 105 J/kg. What is the mass of water in the cup, if the final temperature is −25.0°C?

_______ g

Mass of copper block = mc = 400 g = 0.4 kg

Initial temperature of copper = Tc = 77 K = -196 oC

Mass of water = mw

Initial temperature of water = Tw = 50 oC

Final temperature of mixture = T = -25 oC

Freezing temperature of water = Tf = 0 oC

Specific heat of liquid water = Cw = 4186 J/(kg oC)

Specific heat of solid water = Ci = 2060 J/(kg oC)

Specific heat of copper = Cc = 385 J/(kg oC)

Latent heat of fusion of water = L = 3.35 x 105 J/kg

The heat lost by water is the heat gained by copper.

mcCc(T - Tc) = mwCw(Tw - Tf) + Lmw + mwCi(Tf - T)

(0.4)(385)(-25 - (-196)) = mw[4186(50 - 0) + (3.35x105) + 2060(0 - (-25)]

26334 = mw(209300 + 335000 + 51500)

mw = 0.0442 kg

mw = 44.2 grams

Mass of water in the cup = 44.2 grams

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