Question

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

All of it

400 grams

300 grams

200 grams

100 grams

Answer 1

77K is the the boiling point of N2
specific heat of water = C= 4186 J/kgC

heat of fusion of ice is 334 kJ/kg
Heat of Vaporization N2= Lv= 199.1 kJ/kg


E1 = energy to vaporize N2 = m Lv

E1= 199.1 kJ/kg x 0.5kg = 99.6 kJ
E2 = energy to move water from 15C to 0C = m C dT
= 4.186 kJ/kgC x 0.5 x( 0-15) = -31.40 kJ

negtaive sign shows that this energy is lost by water

So more enrgy required to freeze water=99.6 - 31.4 = 68.2 kJ which will come from freezing of water

let M be the mass of water which freezes

68.2 kJ = 334 kJ/kg x M
M = 0.204 kg

s0 0.204 kg or 204 grams of water are frozen