# Calculate the final temperature of the ice cream

1. Nov 10, 2007

### karr

1. The problem statement, all variables and given/known data
5L of liquid nitrogen @ -205 degree celsius and 1L of liquid ice cream @ 15 degree celsius - they are both mixed. upon mixture nitrogen evaporates and ice cream hardens or freezes. Assuming only 14% of the energy gained by the nitrogen in the process of warming to room temperature (25c) was absorbed from the cream mixture, calculate the final temperature of the ice cream.

2. Relevant equations
Info for Nitrogen:
density = .807g/ml
boiling point N = -195.8c
melting point = -210c
delta H vaporation=199.1 J/g
specific heat of liquid N=1.04j/g*c

Info for Ice cream
density- 1.032g/ml
melting point=-.540c
boiling point=100.17c
specific heat liquid=3.93J/g*c
specific heat solid=2.042J/g*c

(c= degree celsius)

3. The attempt at a solution
I know that they both have to reach a equilibrium and i can carry out the problem from there but the 14% and room temp are throwing me off, how do i use that info?

T(final) = (Mn*S*Tinitial n - Mc*S*Tinitial c)/(-Mn*S+Mc*S)
s=specific heat
Mn= mass of nitrogen
T=temp
c=ice cream

is there anything wrong that I am doing in this equation? plz reply ASAP
thnx

Last edited: Nov 10, 2007
2. Nov 11, 2007

### eli64

wicked problem

from what I can see there are 2 parts:

1. calculate delta H for the nitrogen as it warms up = delta H (absorbed)

this involves 3 steps

a) from -205c to boiling pt N2 \
b) heat of vap of N2
c) from boiling pt to room temp

this is total delta H for N2 = a + b + c

2. since the N2 got only 14% of its energy from the cream mixture, then (this might be a leap) 14% of the total delta H for N2 would be the energy that the cream released as it became ice-cream

so that 14% of total delta H for N2 = delta H of ice-cream

this has 2 steps

d. delta H (liquid at 25C--> solid at mp)
e.delta H (solid at mp --> s at final t)

delta H ice-cream = d + e

you should be able to get d) from your data, you have the delta H of ice-cream, solve for e and final T

usually there is a term for delta H fusion (melting) and that is not given here, but since ice-cream is not a pure-substance, it may not be needed

p.s. watch your signs as you work this out

Last edited: Nov 11, 2007
3. Nov 11, 2007

### karr

srry i forgot to post the delta H fusion of ice cream is 85.272J/g

4. Nov 11, 2007

### eli64

well there you go then, add that into the delta H of the icecream

5. Nov 11, 2007

### karr

thank you so much, u r great!