Pressure depends on distance as - P- alpha- beta- exp - alpha-z-k theta- where alpha- beta- are constants- z is distance- k is Boltzmann constant and theta- is temperature- Calculate the dimensions of beta-

As exponential should be dimentionless Dimension of alpha;=dimention of kÆŸ/z [ alpha;] =[k][z] 1[ÆŸ] nbsp; ——(1) Dimension of k can be obtained by us ...

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Standard XII

Physics

Bernoulli's Principle

Pressure depe...

Question

Pressure depends on distance as , P= α/β exp (-αz/kθ), where α,β are constants, z is distance, k is Boltzmann constant and θ is temperature. Calculate the dimensions of β.

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Solution

As exponential should be dimentionless
Dimension of α=dimention of kÆŸ/z
[α] =[k][z]^-1[ÆŸ] ------(1)
Dimension of k can be obtained by using kinetic energy=3/2kT
[k]=[m¹L²T^-2][K^-1]
[z]=[L¹]
[ÆŸ]=[K]
Putting in equation 1
[α]= [m¹L¹T^-2]

As exponential is dimention less the dimention of P=dimention of α/β
^[β]= [α][p]^-1
⁼[m¹L¹T^-2][mL^-1 T^-2]^-1
[L²]

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