Suppose we pour 5 g of water at 295 k into an insulated container holding a large amount of liquid nitrogen at 77 k. how much nitrogen gets boiled off?

5 g of water of 295 K
boiling point of nitrogen = 77 K = 196 °C
latent heat of vaporization of nitrogen = 199 kJ/kg
heat required for water from 295 K to 77 K
latent heat of water = 334 kJ/kg
specific heat of ice = 2.1 kJ/kh K
specific heat of water = 4.2 kJ/kg K
Total heat required = 334 + (2.1 x 196) + (4.2 x 22) x 5
                              = 4190 J
m x 199 x 10³ = 4190

So m = 21.05 g of nitrogen vaporizes  

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