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Standard XII
Physics
Dimensional Analysis
Question
In the relation,
P
=
α
β
e
α
z
/
k
θ
P
is pressure,
Z
is distance,
K
is Boltzmann constant and
θ
is the temperature. The dimensions of
β
will be
[
M
∘
L
2
T
0
]
[
M
L
2
T
]
[
M
L
∘
T
1
]
[
M
∘
L
2
T
−
1
]
A
[
M
∘
L
2
T
0
]
B
[
M
∘
L
2
T
−
1
]
C
[
M
L
2
T
]
D
[
M
L
∘
T
1
]
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Solution
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P
=
α
β
e
α
z
k
θ
The dimension of power of e is zero.
α
z
k
θ
=
[
M
0
L
0
T
0
]
Thus unit of:
α
=
k
θ
z
Unit of boltzman's constant K is
K
=
[
M
1
L
2
T
−
2
K
−
1
]
By putting thes values we get,
Unit of
α
=
[
M
1
L
2
T
−
2
K
−
1
]
[
K
1
]
[
L
1
]
=
[
M
1
L
1
T
−
2
K
0
]
Therefore unit of
P
=
α
β
Unit of
β
=
α
P
β
=
[
M
1
L
1
T
−
2
K
0
]
[
M
1
L
−
1
T
−
2
]
=
[
M
0
L
2
T
0
]
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P
=
α
β
e
α
z
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k
θ
P
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Z
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K
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θ
is the temperature. The dimensions of
β
will be
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