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Thermodynamics doubt

Doubt question:Find the rate \(v\) with which helium flows out of a thermally insulated vessel into vacuum through a small hole. The flow rate of gas inside the vessel is assumed to be negligible under these conditions. The temperature of Helium in the vessel is \(1000 K\).


Irodov: 2.42


My approach to the problem is stated as under.

The answer provided, unfortunately, turns out to be \(3.3 km/s\). Please help me finding my error out, thanks.

Note by Swapnil Das
3 weeks ago

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bhai tera tarika thik hai par tu pressure eergy wali term bhul raha hai matlab tune pressure ka kuch kiya hi nahi that's a blunder ! @Swapnil Das Shubham Dhull · 1 week, 2 days ago

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https://books.google.co.in/books?id=t8-TM8KTr-sC&pg=PA279&lpg=PA279&dq=Find+the+rate+with+which+helium+flows+out+of+a+thermally+insulated+vessel+into+vacuum+through+a+small+hole.+The+flow+rate+of+gas+inside+the+vessel+is+assumed+to+be+negligible+under+these+conditions.+The+temperature+of+Helium+in+the+vessel+is+.&source=bl&ots=A0vKKyQuLC&sig=bLnTtYZLz6nysMyxpTaYrbhG4g8&hl=en&sa=X&ved=0ahUKEwi5upPzra3QAhVErI8KHe39BVoQ6AEIIDAB#v=onepage&q=Find%20the%20rate%20with%20which%20helium%20flows%20out%20of%20a%20thermally%20insulated%20vessel%20into%20vacuum%20through%20a%20small%20hole.%20The%20flow%20rate%20of%20gas%20inside%20the%20vessel%20is%20assumed%20to%20be%20negligible%20under%20these%20conditions.%20The%20temperature%20of%20Helium%20in%20the%20vessel%20is%20.&f=false Vishwash Kumar · 2 weeks, 3 days ago

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I think you should use Bernoulli's theorem here, and by using it equate the sum of initial pressure energy and internal energy with the final kinetic energy. Maybe then you will get the correct answer. Swagat Panda · 3 weeks ago

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