How we can prove boltzman constant?

[phys111]

hello all

if some one here can help me to prove boltzman costant

from SI unit to reach that k= 1.0356 x 10-22 Torr-liter/K ?

 

[alxm]

I don't know how you can 'prove' an experimental value. But I can tell you how to measure it.

Simplest way would just be to measure the Ideal Gas Constant, since that's just Boltzmann's constant in disguise ($$R = N_Ak_B$$). Take a fixed amount of a relatively ideal gas (e.g. helium) at a fixed volume. Vary the temperature and measure the pressure. Plot p against T and the slope is N*kB.

 

[phys111]

thanks

but i need just to calculate it ?

 

[alxm]

I don't know what you expect to calculate it from? It's a physical constant, not a mathematical one. It's the fundamental relationship between energy and temperature. For different units of either, it wouldn't be needed at all.

The Kelvin scale of temperature is defined by the triple point of water, and so the Boltzmann constant in SI units is determined by that as well.

 

[phys111]

we can start from this relation

PV=N KT

& use convert from SI unit to This unit but i don't reach for the same result

 

[alxm]

Oh sorry, I thought you meant to somehow calculate it. You're saying you want to convert units.

Well if your pressure and volume is in SI units, pV = Pa*m³, so if you want it in Torr-liters you want to multiply by Pascal/Torr and liters/m³.
So (1/133.322368)*1000.

So 1.3806504E-23 (Pa*m³) =1.380 6504E-23*(1000/133.322368) (Torr*Liters) = 1.03513E-22 (Torr*Liters)

 

[phys111]

yes , right

but i don't understand
1.3806504E-23 (Pa*m3)
how you found it
if u can explane to me more

 

[Redbelly98]

yes , right

but i don't understand
1.3806504E-23 (Pa*m3)
how you found it
if u can explane to me more

That is the accepted value in SI units, which anybody can find using Google. The value is given by many sources:

http://physics.nist.gov/cgi-bin/cuu/Value?k
http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/funcon.html
​

It is not clear what the source of your confusion is. Do you want to know:

• How is k determined experimentally?
• Where can you look up the value of k?
• Why are the units Pa*m³/K ?
• Other?

 

[phys111]

thanks

we can find that from Boyle's Law

right