
#1
May2505, 07:43 AM

P: 4

how is that homogenous with respect to units?
i cant get it! 



#2
May2505, 08:41 AM

Sci Advisor
HW Helper
P: 1,772

I don't understand the question. "Homogenous" means "the same everywhere." This equation represent the "universal gas law" which by its title implies it is "the same everywhere." Somehow, I don't think that this is what the question is after. Can you give us the full question?




#3
May2505, 08:50 AM

P: 241

Rev Prez 



#4
May2505, 11:17 AM

Sci Advisor
HW Helper
P: 1,937

how is that homogenous with respect to units?
My guess is that the word "homogeneous" here means that the variables in the equation (P,V,T) are the same thoughout the medium, and do not vary from point to point as would happen before they reach thermodynamic equilibrium.




#5
May2505, 01:30 PM

P: 4

sorry
homogenous with respect to units! 



#6
May2505, 01:57 PM

Sci Advisor
HW Helper
P: 11,863

It looks weird.It makes no sense with "homogeneity",even in Euler sense.
Daniel. 



#7
May2505, 04:00 PM

Mentor
P: 40,905

If so: What are the standard units of each quantity? 



#8
May2505, 04:08 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

To the OP : Write the dimensions in terms of [M], [L] and [T] for each quantity on both sides and check that the final dimensions are the same. [P] (pressure) = [force] / [area] = [mass] [acceleration] [L^2] = ([M] [length] / [time^2]) * [L^2] = [M] [L^1] [T^2] Do the others similarly (and get the units for R correct) 



#9
May2605, 02:36 AM

Sci Advisor
HW Helper
PF Gold
P: 562

amimeera:
What I'm guessing you meant to ask is: Is the equation PV = nRT dimensionally correct? In other words, do the "units" on both sides of the equation match? The answer is: Yes. In SI units we have: P is in Pascals. 1 Pa = 1 N m^2 = 1 kg m^1 s^2 V is in cubic metres (m^3). Therefore PV has units kg m^2 s^2, which is the same as Joules. Another way to say that is that the dimension of PV is the same as energy. n has no units. R is the gas constant, with units J K^1. Temperature is in Kelvin (K). nRT therefore has units of Joules, or dimensions of energy. Since PV and nRT both have dimensions of energy, the equation PV=nRT is dimensionally correct. 


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