A molecule of a substance has a permanent electric dipole moment of magnitude `10^(-29) `C m. A mole of this substance is polarized at low temperature by appling a strong elecrostatic field of magnitude `10^(6) V m^(-1)`. The direction of the field is suddenly changed by an angle of `60^(@)`. Estimate the heat released by the substance in aligning its dipole along the new direction of the field. For simplicity, assume `100%` polarisation of sample.

Explanation

To solve the problem, we need to calculate the heat released when the dipoles in a substance align themselves with a new direction of an electric field after it has been changed. Here’s a step-by-step solution:

### Step 1: Calculate the total dipole moment (P) of the substance
Given:
- The dipole moment of a single molecule, \( p = 10^{-29} \, \text{C m} \)
- Number of molecules in one mole, \( N_A = 6 \times 10^{23} \)

The total dipole moment \( P \) for one mole of the substance is given by:
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