A copper block with a mass of 600 grams is cooled to 77K by being immersed in li

Question

A copper block with a mass of 600 grams is cooled to 77K 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 x 105 J/kg.

I solved for maximum mass of of water and got 216.32 g but how do you find the minimum mass of water that could be in the cup?

Explanation / Answer

(ii)for minimum possible mass of water
at 0 degree, whole water is in solid form
(mcopper)* (Ccopper) * (T)copper = (mwater)* (Cwater) * (T)water + mwater * (Latent heat)water
0.6*385*(273-77) = mmin *4186*(323-273) + mmin * 3.35 * 105
=> mmin = 83.18 grams.

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