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The van der Waal's equation of state for...

The van der Waal's equation of state for 1 mole real gas is `(P + (a)/(V^(2))) (v - b) = RT`....(i)
The Virial equation for 1 mole real gas is `PV = RT [1 + (x)/(V) + (y)/(V^(2)) + (z)/(V^(3))+....." To higher power of " V]` ....(ii)
when x, y and z are constants which are known as 2nd, 3rd adn 4th co-efficients respectively. The temperature at which real gas obeys ideal gas equation i.e., `(PV = nRT)` is known as Boyle's temperature.
Answer the following questions on the basis of the above write up :
If equation (ii) can be one of the way of writing of equation (i), then what will be the value of y?

A

`b - (a)/(RT)`

B

`b^(2)`

C

`b^(3)`

D

`a - (RT)/(b)`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • The van der Waal's equation of state for 1 mole real gas is (P + (a)/(V^(2))) (v - b) = RT ....(i) The Virial equation for 1 mole real gas is PV = RT [1 + (x)/(V) + (y)/(V^(2)) + (z)/(V^(3))+....." To higher power of " V] ....(ii) when x, y and z are constants which are known as 2nd, 3rd adn 4th co-efficients respectively. The temperature at which real gas obeys ideal gas equation i.e., (PV = nRT) is known as Boyle's temperature. Answer the following questions on the basis of the above write up : Which of the following is the incorrect statement about the Boyle's temperature ?

    A
    Temperature at which first virial co-efficient become zero
    B
    Temperature of which first virial coefficient is RT
    C
    Temperature at which third virial co-efficient vanishes
    D
    Both A and C

  • The van der Waal's equation of state for 1 mole real gas is (P + (a)/(V^(2))) (v - b) = RT ....(i) The Virial equation for 1 mole real gas is PV = RT [1 + (x)/(V) + (y)/(V^(2)) + (z)/(V^(3))+....." To higher power of " V] ....(ii) when x, y and z are constants which are known as 2nd, 3rd adn 4th co-efficients respectively. The temperature at which real gas obeys ideal gas equation i.e., (PV = nRT) is known as Boyle's temperature. Answer the following questions on the basis of the above write up : The third virial coefficient of He gas is 4 xx 10^(-2) ("litre/mole")^(2) , then what will be volume of 2 mole He gas at NTP

    A
    22.0 litres
    B
    44.0 litre
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    D
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  • The van der Waal's equation of state for 1 mole real gas is (P + (a)/(V^(2))) (v - b) = RT ....(i) The Virial equation for 1 mole real gas is PV = RT [1 + (x)/(V) + (y)/(V^(2)) + (z)/(V^(3))+....." To higher power of " V] ....(ii) when x, y and z are constants which are known as 2nd, 3rd adn 4th co-efficients respectively. The temperature at which real gas obeys ideal gas equation i.e., (PV = nRT) is known as Boyle's temperature. Answer the following questions on the basis of the above write up : If the critical temperature of the gas be T_(C) = (8a)/(27 Rb) and T_(B) is the Boyle's temperature, then which of the following is the correct relation between T_(C) " and " T_(B) ?

    A
    `T_(C) = (8)/(28) T_(B)`
    B
    `T_(C) = (27)/(8) T_(B)`
    C
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