The magnetic susceptibility of a paramagnetic substance at `-173^(circ) C` is `1.5 xx 10^(-2)`. If its value at `-73^(circ) (C)` is `b xx 10^(-3)` then find `b`.

Answer

To solve the problem of finding the value of \( b \) given the magnetic susceptibility of a paramagnetic substance at two different temperatures, we can use the Curie's Law, which states that the magnetic susceptibility \( \chi \) of a paramagnetic material is inversely proportional to its temperature \( T \) in Kelvin.

### Step-by-Step Solution:

1. **Convert the temperatures from Celsius to Kelvin:**
- The temperature at \( -173^\circ C \) is:
\[ T_1 = -173 + 273 = 100 \, K \]
- The temperature at \( -73^\circ C \) is:
\[ T_2 = -73 + 273 = 200 \, K \]

2. **Use the relationship from Curie's Law:**
- According to Curie's Law:
\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]
- Here, \( \chi_1 = 1.5 \times 10^{-2} \) and \( \chi_2 = b \times 10^{-3} \).

3. **Substitute the values into the equation:**
\[ \frac{1.5 \times 10^{-2}}{b \times 10^{-3}} = \frac{200}{100} \]
- Simplifying the right side:
\[ \frac{1.5 \times 10^{-2}}{b \times 10^{-3}} = 2 \]

4. **Cross-multiply to solve for \( b \):**
\[ 1.5 \times 10^{-2} = 2b \times 10^{-3} \]
- Rearranging gives:
\[ b = \frac{1.5 \times 10^{-2}}{2 \times 10^{-3}} = \frac{1.5}{2} \times 10^{1} = 0.75 \times 10^{1} = 7.5 \]

5. **Final answer:**
\[ b = 7.5 \]

### Summary:
The value of \( b \) is \( 7.5 \).