Acopper 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:

mass of copper block  = 0.3 kg at 77 K or -196 °C

Let mass of water taken be m ( maximum) , in this case we will have mixture of water and copper block at 0°C finally.

Heat gained by copper block

= msΔt

.3 x 196 x 385 J

heat lost by water to lower its temp fro 50°C to 0°C

= m x 4186 x 50

Heat lost = heat gained

m x 4186 x 50 = .3 x 196 x 385

m = 108.16 gm

Let mass of water taken be m ( minimum ) , in this case we will have mixture of ice  and copper block at 0°C finally.

heat lost by water to lower its temp fro 50°C to 0°C

= m x 4186 x 50

heat lost by water to lower its temp from 0°C to 0°C ice

= m x latent heat of fusion

m x 3.35 x 10⁵

Total heat lost

= m x 3.35 x 10⁵ + m x 4186 x 50

= 544300 m

Heat gained by copper block

= msΔt

.3 x 196 x 385 J

Heat lost = heat gained

544300 m = .3 x 196 x 385 J

m = 41.6 gm

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