1. The problem statement, all variables and given/known data *All units given are in standard SI units unless otherwise specified.* *Assume a closed system* How much of -200ºC Liquid Nitrogen is required to completely freeze 200mL (0.2kg) of pure liquid water at 0.00ºC (No change in heat, only a change in state)? Given Values. n= Liquid nitrogen w= Liquid water C= Specific heat capacity Lf= Latent Heat of fusion Lv= Laten Heat of vaporization Cw=4.2E3 Cn= 1.1E2 Lvn=2.0E5 Lfw=3.3E5 Melting point of Nitrogen= -209.9ºC Condensation point of Nitrogen= -196.8ºC 2. Relevant equations Q=mcΔT Q=mLv Q=mLf Conservation of thermal energy. 3. The attempt at a solution Here is my thought process, Ideally, a logical and arithmetical check would be much appreciated. Since we know the water cannot change temperature and instead, only states (L-S), we can state a "restriction" saying that all energy which will convert the unknown mass of nitrogen "mn" will be the absolute value of the energy the water will give off during the mw*Lfw process. By extension, this also means that the all the stage changes which occur to the Nitrogen to get it to zero need to add up to mw*Lfw So... (skipping two steps and common factoring the unknown mass N and isolating for it) we get: Mn=[Mw*Lfw]/[Cn*(3.2)+Lvn+Cn*(196.8)] Plugging in given values in section 1 I get mass as being 0.29729kg. If anyone could confirm this both numerically and the process itself logically, It would be truly appreciated.