Register to reply

How is that homogenous with respect to units?

by amimeera
Tags: homogenous, pvnrt, respect, units
Share this thread:
amimeera
#1
May25-05, 07:43 AM
P: 4
how is that homogenous with respect to units?
i cant get it!
Phys.Org News Partner Physics news on Phys.org
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond
Chi Meson
#2
May25-05, 08:41 AM
Sci Advisor
HW Helper
Chi Meson's Avatar
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?
Rev Prez
#3
May25-05, 08:50 AM
P: 241
Quote Quote by amimeera
how is that homogenous?
i cant get it!
The scalar field describing the gas property (in this case temperature) is homogenous.

Rev Prez

Meir Achuz
#4
May25-05, 11:17 AM
Sci Advisor
HW Helper
PF Gold
P: 2,015
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.
amimeera
#5
May25-05, 01:30 PM
P: 4
sorry
homogenous with respect to units!
dextercioby
#6
May25-05, 01:57 PM
Sci Advisor
HW Helper
P: 11,928
It looks weird.It makes no sense with "homogeneity",even in Euler sense.

Daniel.
Doc Al
#7
May25-05, 04:00 PM
Mentor
Doc Al's Avatar
P: 41,477
Quote Quote by amimeera
sorry
homogenous with respect to units!
So... is the issue how to show that the units match on both sides?

If so: What are the standard units of each quantity?
Gokul43201
#8
May25-05, 04:08 PM
Emeritus
Sci Advisor
PF Gold
Gokul43201's Avatar
P: 11,155
Quote Quote by Doc Al
So... is the issue how to show that the units match on both sides?
I'm pretty sure it is...

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)
James R
#9
May26-05, 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.


Register to reply