In the relation, p = (α/β) e-(α Z/kθ) p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

Question

In the relation, p = (α/β) e-(α Z/kθ) p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be (A)  [ M0 L2 T0 ]  (B)  [ ML2 T]  (C)  [ M L0 T - 1 ]  (D)  [ M0 L2 T - 1 ]

Tardigrade Admin · Accepted Answer

[(α Z/k θ)]=[ M 0 L 0 T 0] [α]=[(k θ/Z)] Further [p]=[(α/β)] ∴[β]=[(α/p)]=[(k θ/Z p)] Dimensions of k θ are that to energy. Hence, [β]=[( ML 2 T -2/ LML -1 T -2)]=[ M 0 L 2 T 0]

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

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

$[M L^{2} T]$

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

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

$[\frac{α Z}{k θ}] = [M^{0} L^{0} T^{0}]$
$[α] = [\frac{k θ}{Z}]$
Further
$[p] = [\frac{α}{β}]$
$∴ [β] = [\frac{α}{p}] = [\frac{k θ}{Zp}]$
Dimensions of $k θ$ are that to energy. Hence,
$[β] = [\frac{M L ^{2} T ^{- 2}}{L M L ^{- 1} T ^{- 2}}] = [M^{0} L^{2} T^{0}]$

Q. In the relation, p=βα​e−kθαZ​ p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

[M0L2T0]

[ML2T]

[ML0T−1]

[M0L2T−1]