Respuesta :
Answer:
The dimensions of a is L⁵·M·T⁻²mol⁻²
Explanation:
The gas equation for a real gas, can be presented as follows;
[tex]\left (P + \dfrac{n^2 \cdot a}{V^2} \right) \cdot \left (V - n \cdot b\right) = R \cdot T[/tex]
Where;
P = The pressure
V = The volume
a = A constant representing intermolecular forces
b = A constant representing molecular volume
n = The number of moles
The dimensions of the expression [tex]P + \dfrac{n^2 \cdot a}{V^2}[/tex] is in units of pressure, given that 'P' is in units of pressure, bar, therefore, the expression, [tex]\dfrac{n^2 \cdot a}{V^2}[/tex], is also measured in units of pressure
The dimensions of pressure, P = M·L⁻¹·T⁻²
'n²' unit dimension is mol², while V² is measured as liter² (L³), therefore, 'a' will convert the units of n² and V² to bars, therefore, we have;
The unit dimension of a = L²·bar/(mol²)
(L³)²·(M/(L·T²))/(mol²) = L⁵·M·T⁻²mol⁻²
The dimension of a = L⁵·M·T⁻²mol⁻²
Where;
L = Length in meters
T = Time in seconds
M = Mass in kilogram
