11 grade physics others

The susceptibility of magnesium at 300 K is 1.2 × 10⁻⁵. At what temperature will the susceptibility increase to 1.8 × 10⁻⁵?

Aniket Singh

1 Year agoGrade

1 Answer

Askiitians Tutor Team

1 Year ago

To solve this problem, we use the relationship between magnetic susceptibility (χ) and temperature (T) for a paramagnetic material, which follows Curie's Law:

χ = C / T

Where:

χ is the magnetic susceptibility.
T is the absolute temperature.
C is the Curie constant (a material-specific constant).
From Curie's Law, we can write the relation for two different conditions:

χ₁ / χ₂ = T₂ / T₁

Here:

χ₁ = 1.2 × 10⁻⁵ (initial susceptibility at T₁ = 300 K)
χ₂ = 1.8 × 10⁻⁵ (new susceptibility at unknown temperature T₂)
Rearranging the equation for T₂:

T₂ = T₁ × (χ₁ / χ₂)

Substitute the known values:

T₂ = 300 × (1.2 × 10⁻⁵ / 1.8 × 10⁻⁵)

Simplify:

T₂ = 300 × (1.2 / 1.8) T₂ = 300 × (2 / 3) T₂ = 200 K

Thus, the temperature at which the susceptibility increases to 1.8 × 10⁻⁵ is 200 K.