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## Homework Statement

A rigid, thermally insulated container with a volume of 22.4 liters is filled with one mole of helium gas (4 grams per mole( at a temperature of 0 Cesius (273K). The container is sitting in a room, surrounded by air at standard temperature and pressure (STP:1atm, 0 Celsius).

a) Calculate the pressure inside the container in N/m^2

b) Calculate the root-mean-square speed of the helium atoms.

c) Now open a tiny square hole in the container, with area 10^-8 m^2. After 5 seconds, how many helium atoms will have left the container?

d) During the same 5 sec. some air molecules from the room will enter the container _ through the same hole. How many air molecules will enter the container?

e) Does the pressure inside the container increase or decrease during this 5 second _ period?

## Homework Equations

a) P=nkT where n=N/V, N is # of molecules (using avagadro's number) and V is in m^3. k is Boltzman's constant, T is temp. in Kelvin.

b) Vrms = sqrt((3kT)/m) where k and T are as above and m is mass.

c) .25nAv[avg] = number of molecules crossing area A per second. n is as above and v[avg] is average velocity.

## The Attempt at a Solution

For part one I calculated 102,716 N/m^2, and for part two I calculated 1.69 * 10^-9 m/s. For part c) I got 5.68*10^8 He atoms escape, and part e, that pressure inside decreases. I am not sure if these answers are right so far, especially the Vrms, as it is so small. The value I got for the pressure 102,716 N/m^2 came directly from the pressure equation above, which I thought should have resulted in atm rather than Pa (N/m^2), but seeing that 102,716 was of the order of magnitude of Pa in this case, I assumed that it was, and left it at that. I wanted to check and make sure I haven't made some grave error. I am also not quite sure how to approach d). Could anyone help? Thanks in advance.

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