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Derivative of Some Standard Functions

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the value of critical temperature in yerms of vanderwaal's cons†an t a and b is given by a)T_c=8a/27Rb b)T_c=27a/8R

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Q. The value of critical temperature in terms of van der Waal's constants

a

b

Q. The value of critical temperature in terms of Van der Waals constant a and b is given by:

Q. Match the following:

List - I	List - II
A. Inversion temperature	(i) $a / R b$
B. Boyle's temperature	(ii) $8 a / 27 R b$
C. Critical temperature	(iii) $2 a / R b$

Q. Assertion :The numerical values of

P_{c}, V_{c}, T_{c}

\frac{a}{27 b^{2}}, 3 b

\frac{8 a}{27 R b}

respectively. Reason: The compressibility factor

Z

at critical conditions is

\frac{3}{8}

.

The essential conditions for liquefaction of gases were discovered by Andrews in

1869

as a result of his study of pressure-volume-temperature relationship for

C O_{2}

. It was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature

(T_{c})

. The pressure required to liquefy a gas at this temperature is called the critical pressure

(P_{c)}

. The volume occupied by one mole of the substance at the critical temperature and pressure is called critical volume. Critical constants are related with van der Waals' constant as follows:

V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}, T_{c} = \frac{8 a}{27 R b}

.

Which of the following parameters is three times the van der Waals' constant

^{'} b^{'}

?

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