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

In summary, the problem involves a souffle being heated from 283.15K to 463.65K, where the air inside expands as an ideal gas. The volume after heating is 1.4 times the original volume. The goal is to find the fraction of the souffle that is air before and after heating. Using PV=T and PV=nRT, and assuming constant pressure, it is possible to write an equation for the volume of the souffle after expansion in terms of the original volumes of air and other ingredients. To solve for this, the increase in air volume (x) from 283.15K to 463.65K is needed, with the assumption that the quantity of air remains constant
  • #1
skate_nerd
176
0

Homework Statement



Okay so I'm trying to figure out how to get this answer. Theres 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

Vtotal=Vair+Vother
therefore
Vtotal-o=Vair-o+Vother
Vtotal-f=Vair-f+Vother
also
Vother-o=Vother-f
Vtotal-f=1.4Vtotal-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=(Vair-f - Vair-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.
 
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  • #2
Is the pressure constant during the heating?

ehild
 
  • #3
skate_nerd said:
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=(Vair-f - Vair-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
 

1. What is the ideal gas law?

The ideal gas law is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is represented by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

2. What is an ideal gas expansion problem?

An ideal gas expansion problem is a type of thermodynamics problem that involves calculating the change in pressure, volume, temperature, or number of moles of an ideal gas during a process. These problems typically use the ideal gas law to solve for unknown variables or to determine the final state of the gas.

3. What are the assumptions of an ideal gas expansion problem?

The ideal gas law assumes that the gas molecules are point masses with no volume, that there are no intermolecular forces between the gas molecules, and that the collisions between molecules and with the container walls are perfectly elastic. It also assumes that the gas is in a closed, rigid container and that the temperature and number of moles of the gas remain constant.

4. How do you solve an ideal gas expansion problem?

To solve an ideal gas expansion problem, you first need to identify the known and unknown variables and choose an appropriate form of the ideal gas law to use. Then, you can plug in the known values and solve for the unknown variable. It may also be helpful to draw a diagram or use a graph to visualize the process and understand the relationships between the variables.

5. What are some real-world examples of ideal gas expansion problems?

Real-world examples of ideal gas expansion problems include the expansion of a gas in a piston, the release of a compressed gas from a canister, and the heating of a gas in a closed container. These types of problems are commonly used in fields such as chemistry, physics, and engineering to study the behavior of gases in different processes and systems.

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