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For a gas obeying the van der Waals' equ...

For a gas obeying the van der Waals' equation, at the critical point

A

both `((delP)/(delV))_(T)`and `((del^(2)P)/(delV^(2)))_(T)`are zero

B

only `((del^(2)P)/(delV^(2)))_(T)` is not zero

C

`((delP)/(delV))_(T)` is zero but `((del^(2)P)/(delV^(2)))_(T)` is non-zero

D

`((delP)/(delV))_(T)` is non-zero but `((del^(2)P)/(delV^(2)))_(T)` is zero

Text Solution

Verified by Experts

The correct Answer is:
a
(a) At critical temperature slope of pressure volume curve is maximum and it is zero.
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At a particular temperature and pressure for a real gas Van der Waal's equation can be written as: (P + a/(V^(2)m)) (V_(m) -b) =RT where Vm is molar volume of gas. This is cubic equation in the variable Vm and therefore for any single value of P & T there should be 3 values of Vm. Which are shown in graph as Q, M and L. As temperature is made to increase at a certain higher temperature the three values of Vm becomes identical. The temperature, pressure & molar volume at point X are called Tc, Pc & Vc for real gas. The compressibility factor in terms of Pc, Vc and T is called Zc. The expression of Van dcr Waal's constant 'a' can be given as

At a particular temperature and pressure for a real gas Van der Waal's equation can be written as: (P + a/(V^(2)m)) (V_(m) -b) =RT where Vm is molar volume of gas. This is cubic equation in the variable Vm and therefore for any single value of P & T there should be 3 values of Vm. Which are shown in graph as Q, M and L. As temperature is made to increase at a certain higher temperature the three values of Vm becomes identical. The temperature, pressure & molar volume at point X are called Tc, Pc & Vc for real gas. The compressibility factor in terms of Pc, Vc and T is called Zc. The value of critical compressibility factor Zc is approximately