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

Question

A copper block with a mass of 300 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. (g)
(b) Calculate the minimum possible mass of water that could be in the cup. (g)

Explanation / Answer

Rate of heat transfer through conduction = m*C*T

m=mass of material

c=specific heat

Here, heat lost from copper = heat gained by water [Energy Conservation]

(i) for maximum possible mass of water:

at 0 degree, whole water is liquid

(mcopper)* (Ccopper) * (T)copper = (mwater)* (Cwater) * (T)water

0.3*385*(273-77) = mmax * 4186*(323-273)

=> mmax = 108.16 grams.

(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

0.3*385*(273-77) = mmin *4186*(323-273) + mmin * 3.35 * 105

=> mmin = 107.98 grams.

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