# Van der waals equation question

• derekmvr
In summary: SI is meters-cubed (m3). So if you are multiplying volume by a number, that number must also have units of volume, which is meters-cubed (m3).This eliminates all of the answers except for L3. [b]So Q1 = A[/b]Q2: The dimensions of a are: a) L6 b) M.L5.T-2 c) M.L-1.T-2 d) M.L-5.T-1 To determine the units of a, we can use the same reasoning as before. (P+a/v2) What are the
derekmvr
Hi everyone,

Struggling with the following question - maths and physics never been my strongest subjects. Thanks in advance

1. An equation of state that has been used to model the behaviour of a fixed amount of a real gas is:
(P+a/v2)(v-b)=ZT
In the equation Z, a, b are constants, and P represents pressure, V = volume, T = temp. The constant Z depends on the amount of gas.
Consider what the dimensions of a and b are in terms of the fundamental quantities of mass (M), length (l), and time (t).

2. Q1: The dimensions of b are:
a) L3
b) L6
c) M.L-1.T-2
d) M-1.L.T2

Q2: The dimensions of a are:
a) L6
b) M.L5.T-2
c) M.L-1.T-2
d) M.L-5.T-1

Q3: The value of the constant Z could be expressed in terms of the unit:
a) W
b) W.N.s-1
c) N.J.K-1
d) J.K-1

3. According to std van der Waal's equantion Z is equivalent of R, therefore Q3 = D, not sure about the calculations for Q1 or Q2

Any help would be greatly appreciated.

Thanks

derekmvr said:
Hi everyone,

Struggling with the following question - maths and physics never been my strongest subjects. Thanks in advance

1. An equation of state that has been used to model the behaviour of a fixed amount of a real gas is:
(P+a/v2)(v-b)=ZT
In the equation Z, a, b are constants, and P represents pressure, V = volume, T = temp. The constant Z depends on the amount of gas.
Consider what the dimensions of a and b are in terms of the fundamental quantities of mass (M), length (l), and time (t).

2. Q1: The dimensions of b are:
a) L3
b) L6
c) M.L-1.T-2
d) M-1.L.T2

I'll help you with this one since it is the easiest. Without just giving you the answer I will explain by analogy. The portion of the equation that contains b is (v-b), right? You are subtracting b from the volume.

Now here is the hint/analogy... Can you subtract gallons from miles? Gallons from degrees C? No. What must the units of b... err be?

## 1. What is the Van der Waals equation?

The Van der Waals equation is a mathematical model used to describe the behavior of real gases, taking into account their non-ideal properties such as volume and intermolecular forces. It was developed in 1873 by Johannes Diderik van der Waals.

## 2. How is the Van der Waals equation different from the ideal gas law?

The ideal gas law assumes that gases behave ideally, meaning they have no volume and do not interact with each other. The Van der Waals equation takes into account the volume of gas particles and the attractive forces between them, leading to a more accurate prediction of gas behavior under non-ideal conditions.

## 3. What are the parameters in the Van der Waals equation?

The Van der Waals equation has two parameters: a and b. The parameter a represents the attractive forces between gas particles and b represents the volume occupied by gas particles. These parameters vary depending on the gas being studied.

## 4. Can the Van der Waals equation be used for all gases?

No, the Van der Waals equation is not applicable to all gases. It is most accurate for gases that have strong intermolecular forces and occupy a larger volume, such as real gases. It is less accurate for gases with weak intermolecular forces and small volumes, such as ideal gases.

## 5. How is the Van der Waals equation derived?

The Van der Waals equation is derived by making modifications to the ideal gas law to account for non-ideal conditions. It takes into account the volume of gas particles and the attractive forces between them, resulting in a more accurate representation of gas behavior. The equation is based on empirical observations and theoretical assumptions.

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