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The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b?
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The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are...
(P + a/v2)(V-b) = RT
where ,
P = Pressure, V = Volume, T = Temperature
a = pv2
a = [ML^-1T^-2][L3]^2
a = [ ML5T^-2 ]
b = v
b = [L^3]
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The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are...
The Dimensional Formula of Constants a and b in the van der Waals Equation
The van der Waals equation is an equation of state that describes the behavior of real gases. It takes into account the attractive forces between gas molecules and the volume occupied by the molecules themselves. The equation is given by:
Where:
- p represents the pressure of the gas
- V represents the volume of the gas
- a is a constant that accounts for the attractive forces between gas molecules
- b is a constant that accounts for the volume occupied by the gas molecules
- R is the ideal gas constant
- T is the temperature of the gas
To determine the dimensional formula of constant a, we need to examine the equation and identify the dimensions of each term.
1. The first term, (p + a/V^2), represents the pressure. The dimensional formula for pressure is [M L^-1 T^-2].
2. The second term, (V - b), represents the volume. The dimensional formula for volume is [L^3].
3. The third term, RT, represents the product of the gas constant and temperature. The dimensional formula for the gas constant, R, is [M L^2 T^-2 K^-1]. The dimensional formula for temperature, T, is [K].
By equating the dimensions on both sides of the equation, we can determine the dimensional formula of constant a:
Simplifying the equation further:
Equating the dimensions on both sides, we find:
Rearranging the equation to solve for a:
Therefore, the dimensional formula of constant a in the van der Waals equation is [M L^5 T^-2].
To determine the dimensional formula of constant b, we apply a similar approach.
1. The first term, (p + a/V^2), represents the pressure and has the dimensional formula [M L^-1 T^-2].
2. The
Introduction
The van der Waals equation is an equation of state that describes the behavior of real gases. It takes into account the attractive forces between gas molecules and the volume occupied by the molecules themselves. The equation is given by:
(p + a/V^2)(V - b) = RT
Where:
- p represents the pressure of the gas
- V represents the volume of the gas
- a is a constant that accounts for the attractive forces between gas molecules
- b is a constant that accounts for the volume occupied by the gas molecules
- R is the ideal gas constant
- T is the temperature of the gas
Determining the Dimensional Formula of Constant a
To determine the dimensional formula of constant a, we need to examine the equation and identify the dimensions of each term.
1. The first term, (p + a/V^2), represents the pressure. The dimensional formula for pressure is [M L^-1 T^-2].
2. The second term, (V - b), represents the volume. The dimensional formula for volume is [L^3].
3. The third term, RT, represents the product of the gas constant and temperature. The dimensional formula for the gas constant, R, is [M L^2 T^-2 K^-1]. The dimensional formula for temperature, T, is [K].
By equating the dimensions on both sides of the equation, we can determine the dimensional formula of constant a:
[M L^-1 T^-2] + a/[L^3]^2 = [M L^2 T^-2 K^-1] [K]
Simplifying the equation further:
[M L^-1 T^-2] + a/[L^6] = [M L^2 T^-2]
Equating the dimensions on both sides, we find:
[M L^-1 T^-2] = a/[L^6]
Rearranging the equation to solve for a:
a = [M L^5 T^-2]
Therefore, the dimensional formula of constant a in the van der Waals equation is [M L^5 T^-2].
Determining the Dimensional Formula of Constant b
To determine the dimensional formula of constant b, we apply a similar approach.
1. The first term, (p + a/V^2), represents the pressure and has the dimensional formula [M L^-1 T^-2].
2. The
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The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b?
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The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b?.
The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The vander wall equation for gas is[p+a/v2] (V-b)=RT where p and V are pressure and volume. Determine the dimensional formula of a constant a and b?.
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