Solving Thermo & Vacuum Problems for Beginners

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A user on Physics Forums presented a problem involving a perfectly insulated box under vacuum that is punctured to fill with air, seeking to determine the final temperature. Initially unsure how to approach the problem, the user later solved it using the equations for work and gas laws. The solution involved calculating work done and applying the ideal gas law to find the final temperature after air enters the box. The discussion highlights the importance of understanding thermodynamic principles in solving such problems. Ultimately, the user successfully resolved their confusion and found the answer.
MattConfused?
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Hi everybody,

i am new to Physics Forums and I have a problem that is confusing me. Any help would be much appreciated.

Problem:

A perfectly insulated box has vacuum inside of it (it is evacuated entirely) and is sitting with standard atmospheric surroundings (1 bar, 298K). It is then punctured and fills with air. What is its final temperature?

I am just not really sure how to approach this. The attempts I have made havn't really got me anywhere.

Thanks,

Matt
 
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Aaaaand I just solved it...

W = (p1)(V1) = m(Cv)(T2-T1) and (p1)(V1) = mR(T1)

Then solved...
 

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