Question

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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

Answer #1

Mass of copper block = m_{c} = 400 g = 0.4 kg

Initial temperature of copper = T_{c} = 77 K = -196
^{o}C

Mass of water = m_{w}

Initial temperature of water = T_{w} = 50
^{o}C

Final temperature of mixture = T = -25 ^{o}C

Freezing temperature of water = T_{f} = 0
^{o}C

Specific heat of liquid water = C_{w} = 4186 J/(kg
^{o}C)

Specific heat of solid water = C_{i} = 2060 J/(kg
^{o}C)

Specific heat of copper = C_{c} = 385 J/(kg
^{o}C)

Latent heat of fusion of water = L = 3.35 x 10^{5}
J/kg

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

m_{c}C_{c}(T - T_{c}) =
m_{w}C_{w}(T_{w} - T_{f}) +
Lm_{w} + m_{w}C_{i}(T_{f} - T)

(0.4)(385)(-25 - (-196)) = m_{w}[4186(50 - 0) +
(3.35x10^{5}) + 2060(0 - (-25)]

26334 = m_{w}(209300 + 335000 + 51500)

m_{w} = 0.0442 kg

m_{w} = 44.2 grams

Mass of water in the cup = 44.2 grams

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Water
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77
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