How is that homogenous with respect to units?

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In summary, the equation PV = nRT is homogenous with respect to units, meaning that the units on both sides of the equation match. This can be shown by breaking down the units for each variable and checking that they all have the same dimensions of energy.
  • #1
amimeera
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how is that homogenous with respect to units?
i can't get it!
 
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  • #2
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
amimeera said:
how is that homogenous?
i can't get it!

The scalar field describing the gas property (in this case temperature) is homogenous.

Rev Prez
 
  • #4
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
sorry
homogenous with respect to units!
 
  • #6
It looks weird.It makes no sense with "homogeneity",even in Euler sense.

Daniel.
 
  • #7
amimeera said:
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?
 
  • #8
Doc Al said:
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)
 
  • #9
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.
 

1. What does it mean for something to be homogenous with respect to units?

Homogeneity with respect to units refers to a property of a system or equation in which all terms have the same units. This means that all the components of the system or equation have consistent units, making it easier to analyze and interpret.

2. Why is it important for something to be homogenous with respect to units?

Homogeneity with respect to units is important because it ensures that all the terms in a system or equation have the same physical dimensions. This helps in accurately understanding and predicting the behavior of the system or equation, as well as in performing calculations and conversions.

3. How can you check if something is homogenous with respect to units?

To check for homogeneity with respect to units, you can analyze the units of each term in the system or equation. If all the units are the same, then the system or equation is homogenous. Alternatively, you can also use dimensional analysis to verify the homogeneity of a system or equation.

4. What are the consequences of something not being homogenous with respect to units?

If something is not homogenous with respect to units, then it means that the components of the system or equation have different units. This can lead to incorrect interpretations, difficulties in performing calculations, and errors in predictions. It is important to ensure homogeneity with respect to units for accurate and consistent results.

5. Can a system or equation be homogenous with respect to units but not physically meaningful?

Yes, a system or equation can be homogenous with respect to units but not physically meaningful. This means that all the terms have the same units, but the overall equation or system does not have any physical significance. Therefore, it is important to not only check for homogeneity with respect to units, but also to ensure that the system or equation is physically meaningful.

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