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The value of compressibility factor at the critical state for a van der Waals gas is
- a)0.325
- b)0.350
- c)0.375
- d)0.400
Correct answer is option 'C'. Can you explain this answer?
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The value of compressibility factor at the critical state for a van de...
Explanation:
The van der Waals equation of state is given by:
(P + a/V^2)(V - b) = RT
Where:
P = Pressure
V = Volume
a = van der Waals constant
b = van der Waals constant
R = Gas constant
T = Temperature
The compressibility factor (Z) is defined as the ratio of the actual molar volume (V) to the ideal molar volume (Videal). It is given by:
Z = PV / RT
At the critical state, the van der Waals gas exhibits special behavior. This is the state at which the gas cannot be liquefied, regardless of the pressure applied. At this state, the van der Waals equation reduces to:
(P + a/V^2)(V - b) = 0
Solving this equation, we get:
V = 3b
P = a/27b^2
Substituting these values into the compressibility factor equation, we get:
Z = PV / RT = (a/27b^2)(3b) / RT = (a/9bRT)
Given that the value of Z at the critical state is 0.375, we can equate this to the above expression and solve for the ratio a/bRT:
0.375 = a/9bRT
Simplifying, we get:
a/bRT = 3.375
Now, the ratio a/bRT is a constant for a given gas. Therefore, we can substitute the value of this constant into the equation to solve for Z:
Z = (a/9bRT) = (3.375)(9) = 30.375
Therefore, the correct answer is option 'C', 0.375.
The van der Waals equation of state is given by:
(P + a/V^2)(V - b) = RT
Where:
P = Pressure
V = Volume
a = van der Waals constant
b = van der Waals constant
R = Gas constant
T = Temperature
The compressibility factor (Z) is defined as the ratio of the actual molar volume (V) to the ideal molar volume (Videal). It is given by:
Z = PV / RT
At the critical state, the van der Waals gas exhibits special behavior. This is the state at which the gas cannot be liquefied, regardless of the pressure applied. At this state, the van der Waals equation reduces to:
(P + a/V^2)(V - b) = 0
Solving this equation, we get:
V = 3b
P = a/27b^2
Substituting these values into the compressibility factor equation, we get:
Z = PV / RT = (a/27b^2)(3b) / RT = (a/9bRT)
Given that the value of Z at the critical state is 0.375, we can equate this to the above expression and solve for the ratio a/bRT:
0.375 = a/9bRT
Simplifying, we get:
a/bRT = 3.375
Now, the ratio a/bRT is a constant for a given gas. Therefore, we can substitute the value of this constant into the equation to solve for Z:
Z = (a/9bRT) = (3.375)(9) = 30.375
Therefore, the correct answer is option 'C', 0.375.
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Community Answer
The value of compressibility factor at the critical state for a van de...
This value comes from the relation, R=(8/3)(p*v/T) where p,v,T are critical values.
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The value of compressibility factor at the critical state for a van der Waals gas isa)0.325b)0.350c)0.375d)0.400Correct answer is option 'C'. Can you explain this answer?
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