To calculate the minimum specific energy of a rectangular channel, we need to use the equation for specific energy:

E = (1/2) * y + (Q^2 / (2 * g * A^2))

where:
E = specific energy
y = depth of flow
Q = discharge
g = acceleration due to gravity
A = cross-sectional area of flow

Given that the critical depth of the rectangular channel is 1.5m, we can use this information to find the specific energy.

1. Calculate the cross-sectional area of flow:
For a rectangular channel, the cross-sectional area is given by the product of the depth and width of the channel.

Let's assume the width of the channel is W.

A = y * W

2. Determine the discharge:
The discharge can be calculated using Manning's equation:

Q = (1 / n) * A * R^(2/3) * S^(1/2)

where:
n = Manning's roughness coefficient
R = hydraulic radius
S = slope of the channel bed

Since the channel is rectangular, the hydraulic radius is given by:

R = A / (2 * (y + W))

3. Substitute the values into the specific energy equation:
Now that we have all the necessary values, we can substitute them into the specific energy equation:

E = (1/2) * y + (Q^2 / (2 * g * A^2))

4. Calculate the specific energy:
Substitute the values of y, A, and Q into the specific energy equation and calculate the minimum specific energy.

5. Compare the result with the given options:
Compare the calculated minimum specific energy with the given options and select the correct one. In this case, the correct answer is option 'b' which states 2.25m.

By following these steps, we can calculate the minimum specific energy of a rectangular channel having a critical depth of 1.5m.