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.

#Mechanics

Easy Math Editor

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Comments

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 - 4 years, 7 months ago

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 - 4 years, 7 months ago

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

A Former Brilliant Member - 4 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$