Perfect Ratio for Solidifying Water: Liquid Nitro vs Water | Simplified Equation

[mtanti]

What ratio of liquid nitrogen to water must there be for total solidification of water (@ RTP)? If there is no static ratio a simplified equation would be nice...
10x!

 

[Gokul43201]

This is a simple energy conservation problem, and might even be homework.

Find the latent heats and the (average/integrated) heat capacity of LN2 from 77K to 273K and use the fact that, under ideal conditions, heat lost by water during cooling and solidification equals the heat gained by LN2 during boiling and warming up (assuming there is still thermal contact between the cold gas and the water - this is unknown as the experimental conditions remain unspecified; else ignore the warming term).