Question

Pressure P varies as P = `alpha/beta "exp" (- (alpha x)/"k"_"BT")`, where x denotes the distance, kB is the Boltzmann's constant, T is the absolute temperature and α and β are constant. The dimension of β is ______.

पर्याय

• [MLT^-2]

• [ML^-1T^-2]

• [M⁰L²T⁰]

• [M⁰L⁰T⁰]

Answer 1

Pressure P varies as P = `alpha/beta "exp" (- (alpha x)/"k"_"BT")`, where x denotes the distance, kB is the Boltzmann's constant, T is the absolute temperature and α and β are constant. The dimension of β is [M⁰L²T⁰].

Explanation:

The power of an exponent is number or constant

∴ Dimensionally `(alpha x)/("k"_"BT")` = [M⁰L²T⁰]

∴ `alpha = (["ML"^2"T"^-2"K"^-1]["K"])/(["L"])` = [MLT^-2]

As k_B = joule/kelvin = [ML²T^-2K^-1] and x = [L]

And dimentionally, `rho = alpha/beta => "B" = alpha/rho`

∴ `["B"] = (["MLT"^-2])/(["ML"^-1"T"^-2])` = [M⁰L²T⁰]

`(therefore rho = "F"/"A" = ["ML"^-1 "T"^-2])`