## Saturday, January 16, 2010

### Irodov Problem 2.2

Initially suppose that chamber 1 has n moles of gas and suppose that the volumes of both chambers is V. Then from ideal gas law we have,

Now both chambers are heated to a temperature of T2 and then the valve let open. Now, gas from chamber 1 starts to flow into chamber 2, until the pressure difference between the chambers is . Suppose that finally, chamber 1 has n1 moles of the gas and chamber 2 has n2 moles of the gas. Let the final pressures in chambers 1 and 2 be, P'1 and P'2. Then we have,

Since the total mass of the gas is conserved we have,

From (1), (2a) , (2b) we can obtain,

From (3a),(3b) and (3) we obtain,

Since the valve opens only when the pressure difference is , we have,

From (4) and (5) we obtain,

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2. Why does not the pressure in both chamber be same after the valve is opened?

1. because the valve will close when the preassure diferente si lower than 1,1 atm

3. Sir valve will open at temp 330 k because at that point pressure difference is 1.1 atm then why not gas diffuse at that time? And also if it open it would be closed within fraction of seconds and process would continue .
Does the question practically possible.

1. Actually according to question valve will be open till the pressure difference is 1.1 and if it is less than that it will close in this way pressure difference can never be zero

4. It has an assumption that the valve was open initially and finally, does this have an explanation