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 - 20.0°C?

mass of copper m = 0.3 kg

Initial temperature t₁ 77K = 77 - 273 = - 196°C

Final temperature t₂ = - 20°C

Mass of water M = ?

Initial temperature of water = 50°C

Final temperature = - 20°C

Heat lost by copper

0.3 x 385 x (-20 + 196)

= 20328 J

Heat lost by water to cool to 0°C

= M x4186 x (50-0)

= 209300 M

Heat lost by water to cool to freeze at 0°C

= M x 335 x 10³ J

Heat lost by ice to cool to - 20°C

= Mx 2060 x 20

= 41200 M

Total heat gained

= 585500 M

Heat lost by water = heat gained by copper block

585500 M = 20328

M =.03472 Kg

= 34.72 g