The susceptibility of paramagnetic fecl3 is 3×10 at 27c what will be its relative permeability at 200k and 500k

To determine the relative permeability of paramagnetic FeCl3 at different temperatures, we can use the relationship between susceptibility and temperature. The susceptibility (χ) of paramagnetic materials is typically inversely proportional to temperature, following Curie's Law. This law states that the susceptibility is proportional to the inverse of the absolute temperature (T), which can be expressed mathematically as:

Understanding Curie's Law

Curie's Law can be formulated as:

• χ = C / T

Where:

• χ is the magnetic susceptibility.
• C is the Curie constant, which is specific to the material.
• T is the absolute temperature in Kelvin.

Given Data

From your question, we know:

• χ at 27°C (300 K) = 3 × 10^-3
• We need to find χ at 200 K and 500 K.

Calculating the Curie Constant

First, we can calculate the Curie constant (C) using the susceptibility at 300 K:

• C = χ × T = (3 × 10^-3) × 300 = 0.9

Finding Susceptibility at Different Temperatures

Now, we can use this constant to find the susceptibility at 200 K and 500 K:

At 200 K:

• χ₂₀₀ = C / T = 0.9 / 200 = 0.0045

At 500 K:

• χ₅₀₀ = C / T = 0.9 / 500 = 0.0018

Calculating Relative Permeability

The relative permeability (μ_r) of a material is related to its susceptibility by the formula:

• μ_r = 1 + χ

Relative Permeability at Different Temperatures

Now, we can calculate the relative permeability at both temperatures:

At 200 K:

• μ_r,200 = 1 + χ₂₀₀ = 1 + 0.0045 = 1.0045

At 500 K:

• μ_r,500 = 1 + χ₅₀₀ = 1 + 0.0018 = 1.0018

Summary of Results

In summary, the relative permeability of paramagnetic FeCl3 at the specified temperatures is:

• At 200 K: μ_r ≈ 1.0045
• At 500 K: μ_r ≈ 1.0018

This demonstrates how the magnetic properties of materials can change with temperature, reflecting the fundamental principles of magnetism in paramagnetic substances.