C 12B 2009 Problem 17: Finding the Fraction of Air in a Heated Souffle

[skate_nerd]

Homework Statement

Okay so I'm trying to figure out how to get this answer. there's a souffle made of some ingredients and filled with these ingredients along with some air. Everything starts off at 283.15 K and gets heated in the oven to 463.65 K. Also assume that the air expands with heat as an ideal gas, and the other ingredients' expansion is negligible. Also the volume after heating up is 1.4 times the volume before heating up.

What we are looking to find is the fraction of the volume of the souffle that is air before being heated up, and the fraction of the volume of the souffle that is air after being heated.

Homework Equations

PV=T
PV=nRT

V_total=V_air+V_other
therefore
V_total-o=V_air-o+V_other
V_total-f=V_air-f+V_other
also
V_other-o=V_other-f
V_total-f=1.4V_total-o

The Attempt at a Solution

So I've messed around with these known equations and legitimately came up with something that I feel is in the right direction of solving the problem. I found that
1=(V_air-f - V_air-o)/0.4. I figure now that I can use PV=T to get this formula in terms of one variable of the air's volume, however I am not really sure how to do that since I have no value for P. I'm assuming also in this problem that being a souffle, when it heats up the top just tightens to keep the pressure constant.

So that's all I got. If somebody could help or point me in the right direction for solving this that would be awesome.

 

[ehild]

Is the pressure constant during the heating?

ehild

 

[Andrew Mason]

So I've messed around with these known equations and legitimately came up with something that I feel is in the right direction of solving the problem. I found that
1=(V_air-f - V_air-o)/0.4. I figure now that I can use PV=T to get this formula in terms of one variable of the air's volume, however I am not really sure how to do that since I have no value for P. I'm assuming also in this problem that being a souffle, when it heats up the top just tightens to keep the pressure constant.

So that's all I got. If somebody could help or point me in the right direction for solving this that would be awesome.

Answer ehild's question and assume that the quantity of air (n) does not change. By what factor does a given volume of air increase in going from 283.15K to 463.65K? Call that x. You can then write out an equation for the volume of the souffle after expansion in terms of the original volumes of air and the original volume of other ingredients.

AM