Heat; Q=mct & Q=mL liquid nitrogren and water

Question

500 grams of liquid nitrogen at 77K is stirred into a beaker containing 500 grams of 15C water. If the nitrogen leaves the solution as soon as it turns to gas, how much water freezes?

Answer 1

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specific heat of water is 4186 J/kgC

heat of fusion of ice is 334 kJ/kg

Heat of Vaporization N2 199.1 kJ/kg

Calculate all the energy numbers involved. 77 is aprox the boiling point of N2

E1 = energy to vaporize N2 = 199.1 kJ/kg x 0.5kg = 99.6 kJ

E2 = energy to move water from 15C to 0C

= 4.186 kJ/kgC x 0.5 x 15 = 31.40 kJ

the difference is 99.6 - 31.4 = 68.2 kJ, which is left to freeze water at 0C

68.2 kJ = 334 kJ/kg x M

M = 0.204 kg

so 0.204 kg out of the 0.5 kg is frozen.

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