Making jam and then putting it into jars is called canning. The process involves putting the jam into the jars while it’s still quite hot; hot enough to kill germs. While canning some strawberry jam you notice that the lid pops in towards the jam when the temperature drops to 90C. The temperature of the jam starts at 110C. The air pressure is 89923 Pa in the room. The diameter of the lid (and jar) is 8.00cm, the height of the jar is 11.9366cm. You put 550cm^3 of jam in each jar.
1. Using the ideal gas law, calculate the pressure of the air inside of the jar if the temperature went from 110C to 90C?
2. What is the average kinetic energy of the gas molecules inside the jar? How does this compare to air in an oven at 90C, in a 10 liter oven (at the same pressure as the room)? (Assume that the molecules have a ~29u both in the jar and in the oven, and are diatomic.)
3. Would you say that the molecules hit each other more or less often than they hit the sides of the jar? You can assume that the molecules have r = 1.0x10-10m.
4. Calculate the mean free path of the molecules in the oven. You can assume that the molecules have r = 1.0x10-10m.
p=F/A , pV=nRT , A=pi(r)^2 , v(rms) = sqrt((3(kb)T)/m) , lamda = 1/4 (sqrt(2))pi(N/V)r^2 ,
Ek = 0.5mv^2 , Eavg = 3/2(kb)T
The Attempt at a Solution
1. For this one, it seems easy enough but I'm not sure how to relate the change in temperature into the solution. The pressure changes as it cools, right? So, how can I settle on one pressure inside the jar?
2. I tried using Ek=0.5mv^2 but, I dont have the mass. So I went to Eavg=3/2(kb)T which is easy enough to solve but, it asks me to relate it to a 10L oven, is the Eavg the same in both, despite the ovens larger volume? Thats what confuses me.
3. No attempt here. I'm not sure in the least.
4. I know the formula for mean free path but, I'm not sure how to get the 10L part into the equation. My (N/V) for the oven would be the same as for the jar since they say use the same pressure and temp but, that doesnt make since since the oven is larger. Shouldnt the free path for the oven be larger?
Very lengthy, I know. Though, any and all help would be appreciated. Thanks.