Relation between energy annd pressure

  • Thread starter Haseeb Ali
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  • #1
Me and and my friend were having discussion about the motion of molecules of gas.We talked about their velocity ,kinetic energy and much more. He asked me to derive a relation between pressure and energy. I was unable to explain him that... Can anyone explain the relation?
 

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  • #2
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He asked me to derive a relation between pressure and energy.
How would you begin? What information do you have?
 
  • #3
How would you begin? What information do you have?
P=density*Vx*2

T= 2/3k 1/2mv*2
 
  • #4
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You could read up on the gas law, e.g. here
Your equations feature in there, but one appears molecular to me and the other macroscopic:

##{1\over 2} mv^2 = {3\over 2} kT## average kinetic energy for a molecule.

##P = \rho v_x^2 = {mass\over V} v_x^2 ## may be ok if in the right context.

I can wrangle a bit with formulas: $$ {1\over 2} mv^2 = {3\over 2} kT\ \Rightarrow\ {1\over 2} mv_x^2 = {1\over 2} kT$$ (the energy is equally distributed over the three degrees of freedom),

##\displaystyle \ \Rightarrow\ v_x^2 = {kT\over m} ##

mass = number of molecules * mass of a molecule = number of moles * ##N_A## * mass of a molecule (Avogadro number); write mass = ##n\; N_A\; m##

Leaves

##pV = n\;N_A\;m \ {kT\over m} = n\; N_A \;kT##;

then use

##R_G = N_A \; k## (gas constant) to get the ideal gas law

##pV = nR_GT##.

pressure times volume has the dimension of energy.

It's not the whole story, but quite a big part of it.
 

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