In the equation `((1)/(pbeta))=(y)/(k_(B)T)`, where `p` is the pressure, `y` is the distance, `k_(B)` is Boltzmann constant and `T` is the tempreture. Dimensions of `beta` are
Correct Answer – B
Given equation, `(1)/(pbeta)=(y)/(k_(B)T)`
where, `p` = pressure, `y` = distance,
`k_(B)` = Boltzmann constant and `T` = temperature
Dimension of `[beta]=([“Dimensions of “k_(B)][“Dimensions of “T])/([“Dimensions of “p][“Dim en sions of “y])`
`” “=([“ML”^(2)”T”^(-3)][“T”])/([“ML”^(-1)”T”^(-2)][“L”])=[“M”^(0)”L”^(2)”T”^(0)]`
`(1)/(p beta) = (y)/(k_(8) T)`
Dimension of
`[beta] = ([“Dimensional formula of” k_(B)][“Dimensional formula of” T])/([“Dimensional formula of p”] [“Dimensional formula of y”])`
`= ([ML^(2) T^(2) K^(-1)][K])/([ML^(-1) T^(-2)][L]) = [M^(0) L^(2) T^(0)]`
`:.` Dimensions of `M,L,T` in `beta` are `0,2,0`