First slide

Accuracy; precision of instruments and errors in measurements

Question

In the relation $P = \frac{α}{β} e^{- α Z / k θ}$ , P is the pressure, Z is the distance, k is the Boltzmann constant and q is the temperature. The dimensional formula of $β$ will be

Moderate

A

$[M^{0} L^{2} T^{0}]$
B

$[M^{1} L^{2} T^{1}]$
C

$[M^{1} L^{0} T^{- 1}]$
D

$[M^{0} L^{2} T^{- 1}]$

Solution

$\begin{array}{l} [\frac{α Z}{K θ}] = [M^{0} L^{0} T^{0}] & [α] = [\frac{K θ}{Z}] \\ But [P] = [\frac{α}{β}] So, [β] = [\frac{α}{P}] = [\frac{K θ}{Z P}] \\ [β] = [\frac{[M L^{2} T^{- 2} θ^{- 1}] [θ]}{[L] [M L^{- 1} T^{- 2}]}] = [M^{0} L^{2} T^{0}] \end{array}$
(Since dimensions of K' is of energy)

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