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Standard XII

Physics

Temperature

Pressure depe...

Question

Pressure depends on distance as $P = \frac{α}{β} e x p (- \frac{α z}{k θ})$ , where $α, β$ are constants, z is distance, k is Boltzmann's constant, and $θ$ is temperature. The dimensions of $β$ are

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

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

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

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

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Solution

The correct option is B $M^{0} L^{2} T^{0}$
$\frac{α z}{k θ}$ is unitless.
$Z \to L$
$α \to M L T^{- 2}$
$\frac{α}{β} = M L^{- 1} T - 2$ (unit of pressure)
$β \to L^{2}$

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Pressure depends on distance as P=αβexp(−αzkθ), where α,β are constants, z is distance, k is Boltzmann's constant, and θ is temperature. The dimensions of β are

The correct option is B M0L2T0αzkθ is unitless.Z→Lα→MLT−2αβ=ML−1T−2 (unit of pressure)β→L2

Pressure depends on distance as $P = \frac{α}{β} e x p (- \frac{α z}{k θ})$ , where $α, β$ are constants, z is distance, k is Boltzmann's constant, and $θ$ is temperature. The dimensions of $β$ are

The correct option is B $M^{0} L^{2} T^{0}$
$\frac{α z}{k θ}$ is unitless.
$Z \to L$
$α \to M L T^{- 2}$
$\frac{α}{β} = M L^{- 1} T - 2$ (unit of pressure)
$β \to L^{2}$