In the relation p = β α e − k θ α Z , p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be (JEE 2004)

Question

In the relation p = β α ​ e − k θ α Z ​ , p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be (JEE 2004)

TestHub · Accepted Answer

k θ α Z ​ is dimensionless, so [ α ] = [ Z k θ ​ ] = [ L ] [ M L 2 T − 2 ] ​ = [ M L T − 2 ] . Then [ β ] = [ p α ​ ] = [ M L − 1 T − 2 ] [ M L T − 2 ] ​ = [ M 0 L 2 T 0 ] .

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