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.
When the system comes to equilibrium, the temperature is 0°C.

(a) Calculate the maximum possible mass of water that could be in the cup.
grams

(b) Calculate the minimum possible mass of water that could be in the cup.
grams

Explanation / Answer

heat absorbed by copper block to come to 273 k from 77k =
385*0.6*(273-77)
=45276 J

the final mix temp is given as 00C

so max amount of water is when water has just reached 00C with out forming ice.

let the mass be X gm

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 10^5 J/kg

4.186*50*X= 45276

X = 216.32 gm

b)

min amount of water is mhen all the water gets converted to ice.

4.186*50*X + 335*X = 45276

X = 83.182 gm

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