Question:
The inversion temperature for a van der Waals gas is given by:
The inversion temperature for a van der Waals gas is given by:
Updated On: Jun 7, 2022
- $ {{T}_{i}}=\frac{2a}{Rb} $
- $ {{T}_{i}}=\frac{a}{Rb} $
- $ {{T}_{i}}=\frac{a}{2Rb} $
- $ {{T}_{i}}=0.5\,{{T}_{Boyle}} $
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The Correct Option is A
Solution and Explanation
Inversion temperature of a van der Waals gas is given by $ {{T}_{i}}=\frac{2a}{Rb}=2{{T}_{b}} $ (where $ {{T}_{b}}= $ Boyle temperature)
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Concepts Used:
Van Der Waals Equation
Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases.
Read More: Derivation of Van Der Waals Equation
Derivation of Van der Waals equation:
For a real gas containing ‘n’ moles, the equation is written as
Where, P, V, T, n are the pressure, volume, temperature and moles of the gas. ‘a’ and ‘b’ constants specific to each gas.
Where,
Vm: molar volume of the gas
R: universal gas constant
T: temperature
P: pressure
V: volume
Thus, Van der Waals equation can be reduced to ideal gas law as PVm = RT.
The equation can further be written as;
- Cube power of volume:
- Reduced equation (Law of corresponding states) in terms of critical constants:
Units of Van der Waals equation Constants
a: atm lit² mol-²
b: litre mol-¹