Question
Question: The critical volume of a gas obeying van der Waals equation is: A. \(\dfrac{8a}{27{{R}_{b}}}\) B...
The critical volume of a gas obeying van der Waals equation is:
A. 27Rb8a
B. 27b2Ra
C. 3b
D. 27Rbq
Solution
The Vander Waals equation for a real gas is as follows.
(P+V2a)(V−b)=RT
Here P = Pressure of the gas
V =Volume of the gas
R = Gas constant
T = Temperature of the gas
a = Attraction between the gas particles
b = the volume excluded
Complete answer:
- In the question it is asked to find about the critical volume of the gas obeying Vander Waals equation among the given options.
- By using the Vander Waals gas equation for real gas, we can find the critical volume of the gas which obeys Vander Waals gas equation.
- The Vander Waals gas equation is as follows.
(P+V2a)(V−b)=RT
Here P = Pressure of the gas
V =Volume of the gas
R = Gas constant
T = Temperature of the gas
a = Attraction between the gas particles
b = the volume excluded
- We can rearrange the above Vander Waals gas equation as follows.
P=V−bRT−V2a
- We know that at critical temperature ∂V∂P=0
- Therefore,