*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)?
n= Liquid nitrogen
w= Liquid water
C= Specific heat capacity
Lf= Latent Heat of fusion
Lv= Laten Heat of vaporization
Melting point of Nitrogen= -209.9ºC
Condensation point of Nitrogen= -196.8ºC
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:
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.