Pressure P varies as P-cfrac - alpha - beta - expleft- cfrac - -alpha - - K - B -theta - Z right- where Z denotes distance- - K - B - Boltzman-s constant-theta temperature and alpha -beta are constants-Derive the dimensions of beta left- - M - -1 - LT - -2 - right- left- - M - 0 - L - 0 - T - 0 - right- left- - M - 0 - L - 2 - T - 0 - right- left- - M - 0 - L - -1 - T - -2 - right-

Question

Pressure P varies as P-cfrac - alpha - beta - expleft- cfrac - -alpha - - K - B -theta - Z right-  where Z denotes distance- - K - B - Boltzman-s constant-theta  temperature and alpha -beta are constants-Derive the dimensions of beta left- - M - -1 - LT - -2 - right- left- - M - 0 - L - 0 - T - 0 - right- left- - M - 0 - L - 2 - T - 0 - right- left- - M - 0 - L - -1 - T - -2 - right-

Toppr Admin · Accepted Answer

-x3B1-ZKB-x3B8-M0L0T0K0-x3B1-KB-x3B8-Z-ML2T-x2212-2K-x2212-1-K-L-x3B1-MLT-x2212-2-P-x3B1-x3B2-x3B2-x3B1-P-MLT-x2212-2ML-x2212-1T-x2212-2-M0L0T0Ans- M0L0T0

Pressure P varies as $P = \frac{α}{β} e x p (\frac{- α}{K_{B} θ} Z)$ where Z denotes distance. $K_{B}$ Boltzman's constant. $θ$ temperature and $α, β$ are constants.Derive the dimensions of $β$
$[M^{- 1} {L T}^{- 2}]$
$[M^{0} L^{0} T^{0}]$
$[M^{0} L^{2} T^{0}]$
$[M^{0} L^{- 1} T^{- 2}]$

$\frac{α Z}{K_{B} θ} = M^{0} L^{0} T^{0} K^{0} α = \frac{K_{B} θ}{Z} = \frac{[M L^{2} T^{- 2} K^{- 1}] [K]}{[L]} α = M L T^{- 2} [P] = \frac{[α]}{[β]} β = \frac{α}{P} = \frac{M L T^{- 2}}{M L^{- 1} T^{- 2}} = M^{0} L^{0} T^{0}$
Ans: $M^{0} L^{0} T^{0}$

Pressure P varies as P=αβexp(−αKBθZ) where Z denotes distance. KB Boltzman's constant.θ temperature and α,β are constants.Derive the dimensions of β[M−1LT−2][M0L0T0][M0L2T0][M0L−1T−2]

αZKBθ=M0L0T0K0α=KBθZ=[ML2T−2K−1][K][L]α=MLT−2[P]=[α][β]β=αP=MLT−2ML−1T−2=M0L0T0Ans: M0L0T0

Pressure P varies as $P = \frac{α}{β} e x p (\frac{- α}{K_{B} θ} Z)$ where Z denotes distance. $K_{B}$ Boltzman's constant. $θ$ temperature and $α, β$ are constants.Derive the dimensions of $β$
$[M^{- 1} {L T}^{- 2}]$
$[M^{0} L^{0} T^{0}]$
$[M^{0} L^{2} T^{0}]$
$[M^{0} L^{- 1} T^{- 2}]$

$\frac{α Z}{K_{B} θ} = M^{0} L^{0} T^{0} K^{0} α = \frac{K_{B} θ}{Z} = \frac{[M L^{2} T^{- 2} K^{- 1}] [K]}{[L]} α = M L T^{- 2} [P] = \frac{[α]}{[β]} β = \frac{α}{P} = \frac{M L T^{- 2}}{M L^{- 1} T^{- 2}} = M^{0} L^{0} T^{0}$
Ans: $M^{0} L^{0} T^{0}$