Dimensional formula of beta in the given relation:

To determine the dimensional formula of beta, we can use the method of dimensional analysis.

Step 1: Write the given relation in terms of fundamental units.

P = alpha/beta e^-alpha X/nR theta

Step 2: Determine the dimensions of each term in the equation.

- P: Power = [M L^2 T^-3]
- alpha: Constant = Dimensionless
- beta: ?
- e: Constant = Dimensionless
- X: Distance = [L]
- n: Number of moles = [Mol]
- R: Gas constant = [M L^2 T^-2 K^-1]
- theta: Temperature = [K]

Step 3: Equate the dimensions on both sides of the equation.

[M L^2 T^-3] = [Dimensionless] / [beta] * [Dimensionless]^[alpha] * [L] / ([Mol] * [M L^2 T^-2 K^-1] * [K])

Simplifying the above equation, we get:

[M L^2 T^-3] = [L] / ([Mol] * [M K^-1 T^-2])

Step 4: Solve for the dimension of beta.

[M L^2 T^-3] * [Mol] * [M K^-1 T^-2] = [L]

[Mol M^2 K^-1 T^-5] = [L T^3]

Therefore, the dimensional formula of beta is [Mol M^2 K^-1 T^-5].

Explanation:

The dimensional formula of a physical quantity represents the power to which the fundamental units of mass, length, and time are raised in that quantity. In the given relation, the term beta is the only term whose dimension is unknown. Therefore, to determine the dimensional formula of beta, we used the method of dimensional analysis. We equated the dimensions on both sides of the equation and solved for the dimension of beta. The resulting dimensional formula of beta is [Mol M^2 K^-1 T^-5]. This means that beta is a combination of moles, square meters, Kelvin, and inverse powers of time.