Pressure depends on distance as P=(α /β )exp((- α z/ K θ )) . Where α ,β are constant, z is distance, K-Boltzman's constant, θ is temperature the dimension of β are :-

Question

Pressure depends on distance as P=(α /β )exp((- α z/ K θ )) . Where α ,β are constant, z is distance, K-Boltzman's constant, θ is temperature the dimension of β are :- (A) M0L0T0 (B) M- 1L- 1T- 1 (C) M0L2T0 (D) M- 1L1T2

Tardigrade Admin · Accepted Answer

K=(J/kelvin)=ML2T- 2θ - 1 (α Z/ K θ )=M0L0T0 [.α ].=MLT- 2θ 0 [P]=([α ]/[β ])⇒ [β ]=([α ]/[P])=(MLT- 2/ML- 1 T- 2)=L2

Q. Pressure depends on distance as $P = \frac{α}{β} e x p (\frac{- α z}{K θ})$ . Where $α, β$ are constant, $z$ is distance, K-Boltzman's constant, $θ$ is temperature the dimension of $β$ are :-

$M^{0} L^{0} T^{0}$

$M^{- 1} L^{- 1} T^{- 1}$

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

$M^{- 1} L^{1} T^{2}$

$K = \frac{J}{k e l v in} = M L^{2} T^{- 2} θ^{- 1}$
$\frac{α Z}{K θ} = M^{0} L^{0} T^{0}$
$[α] = M L T^{- 2} θ^{0}$
$[P] = \frac{[ α ]}{[ β ]} \Rightarrow [β] = \frac{[ α ]}{[ P ]} = \frac{M L T ^{- 2}}{M L ^{- 1} T ^{- 2}} = L^{2}$

Q. Pressure depends on distance as P=βα​exp(Kθ−αz​) . Where α,β are constant, z is distance, K-Boltzman's constant, θ is temperature the dimension of β are :-

M0L0T0

M−1L−1T−1

M0L2T0

M−1L1T2