Question

Pressure depends on distance as $P=\frac{\alpha }{\beta }exp\left(\frac{- \alpha z}{ K \theta }\right)$ . Where $\alpha ,\beta $ are constant, $z$ is distance, K-Boltzman's constant, $\theta $ is temperature the dimension of $\beta $ are :-

• A. $M^{0}L^{0}T^{0}$
• B. $M^{- 1}L^{- 1}T^{- 1}$
• C. $M^{0}L^{2}T^{0}$
• D. $M^{- 1}L^{1}T^{2}$

Answer 1

Answer: (C)

$K=\frac{J}{kelvin}=ML^{2}T^{- 2}\theta ^{- 1}$
$\frac{\alpha Z}{ K \theta }=M^{0}L^{0}T^{0}$
$\left[\right.\alpha \left]\right.=MLT^{- 2}\theta ^{0}$
$\left[P\right]=\frac{\left[\alpha \right]}{\left[\beta \right]}\Rightarrow \left[\beta \right]=\frac{\left[\alpha \right]}{\left[P\right]}=\frac{MLT^{- 2}}{ML^{- 1} T^{- 2}}=L^{2}$