**Question: ** There are 2 flasks of equal volume, connected by a narrow tube of negligible volume, filled with nitrogen gas. When both are immersed in boiling water, the gas pressure inside the system is 0.5 atm. Calculate the pressure of the system when one of the flasks is immersed in ice water mixture, keeping the other in boiling water.
Problem: There are two ways that I am going to describe that I can think of to solve the question, but they give different answers.
Way 1: Net Temperature of the system should be 50 degree Celsius because there is no heat loss and there is symmetry. As both the flasks are identical and at 100 and 0 so it should be 50. Calculating the answer with this assumption and the formula P1/V1=P2/V2 The answer comes out to be about 0.432 atm
Way 2: The sum of the moles of gas in both the flasks would remain same. And using the ideal gas equation to get n = number of moles = PV/RT After equating the values. The pressure come out to be about 0.422 atm
I was bothered with the 0.1 change. So I took the liberty to calculate the temperature from way 2, and it came out to be about 41.82 degree Celsius.
Note : calculations were done in Kelvin itself.
So we assumed that temperature would be 50 but way 2 contradicts that. I could not find a fault in either of the ways so could not understand what temperature would it really be.
Attempt to solve: is it something about Gibbs Paradox? I was Googleing and that came, but I couldn't understand...
Please help with proper explanation on why the other way is wrong.