# Calculate the final temperature of the ice cream

karr

## Homework Statement

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.

## Homework 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)

## 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? please reply ASAP
thnx

Last edited:

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

eli64
srry i forgot to post the delta H fusion of ice cream is 85.272J/g

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

karr
thank you so much, u r great!