A copper block with a mass of 300 grams is cooled to 77 K by being immersed in l

Question

A copper block with a mass of 300 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 ?15.0°C? Give your answer in grams.

Explanation / Answer

Given,

m = 300 g ; T = 77 K = -196 deg C ; Tw = 50 deg C ; Cw = 4186 J/kg-C ; Ci = 2060 J/kg-C ; Cc = 385 J/kg-C. ; Lf = 3.35 x 10^5 J/kg ; Tf = -15 deg C

We know that

Q(lost) = Q(gain)

Mw [Cw delta T + Lf + Ci delta T] = Mc (Cc delta T)

Mw (4186 x 50 + 3.35 x 10^5 + 2060 x 15) = 0.3 x 385 x 181

Mw = 20905.5/575200 = 0.0363 kg

Hence, Mw = 0.0363 kg = 36.3 g

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