dimensional formula of k
Answers
Dimensional Formula of k-
k is the symbol of the Boltzmann Constant.
The dimensional formula of (k) i.e., Boltzmann constant is derived by,
[M1 L2 T-2 K-1]
where,
*M is the Mass.
*K is the Temperature.
*L is the Length.
*T is the Time.
Derivation-
*Boltzmann Constant (k) = Energy × [Temperature]-1 . . . (equation1)
Since,
Energy = M × a × displacement = [M1 × M0 L1 T-2 × L1]
Therefore,
*The dimensions of energy = [M1 L2 T-2] . . . (equation2)
And,
*The dimensional formula of temperature = [M0 L0 T0 K1] . . .(equation3)
By substituting (equation2) and (equation3) in equation (1)
we get,
Boltzmann Constant(k) = Energy × [Temperature]-1
=> k = [M1 L2 T-2] × [M0 L0 T0 K1]-1 = [M1 L2 T-2 K-1].
Therefore,
The Boltzmann constant (k) is dimensionally being represented as-
[M1 L2 T-2 K-1]
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