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## Homework Statement

*All units given are in standard SI units unless otherwise specified.*

*Assume a closed system*

How much of -200

^{º}C Liquid Nitrogen is required to completely freeze 200mL (0.2kg) of pure

__liquid__water at 0.00

^{º}C (No change in heat, only a change in state)?

Given Values.

n= Liquid nitrogen

w= Liquid water

C= Specific heat capacity

L

_{f}= Latent Heat of fusion

L

_{v}= Laten Heat of vaporization

C

_{w}=4.2E3

C

_{n}= 1.1E2

L

_{vn}=2.0E5

L

_{fw}=3.3E5

Melting point of Nitrogen= -209.9

^{º}C

Condensation point of Nitrogen= -196.8

^{º}C

## Homework Equations

Q=mcΔT

Q=mL

_{v 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.}