Find the units and dimensions of constants ‘a’ and ‘b’ in the van der Waal’s equations (+2)(−)= Where P is pressure, V is volume and T is temperature.
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Answer:
We can add and structure only like quantities.
⇒ Dimensions of P = Dimensions of
V
2
a
...... (i)
and dimension of V = Dimensions of b ............ (ii)
From (i),
Dimensions of a = Dimensions of P× Dimensions of V
2
[a]
1
L
−1
T
−2
]×[L
3
]
2
=[M
1
L
5
T
−2
]
Unit of a= Unit of p×Unitofv
2
=
m
2
N
×m
6
=Nm
4
From (ii), [b] = [V]=[M
0
L
3
T
0
]
So unit of b = Unit of V = m
3
Explanation:
We can add and structure only like quantities.
⇒ Dimensions of P = Dimensions of
V
2
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