The susceptibility of magnesium at `27^@C` is `1.2 xx 10^(-5)`. The temperature (in K) at which susceptibility equal to `1.44 xx 10^(-5)` is T. What is the value of `T/10` ?

Explanation

To solve the problem step by step, we will use the relationship between susceptibility and temperature. The susceptibility (χ) of a material is inversely proportional to its temperature (T) according to the formula:

\[ \frac{χ_2}{χ_1} = \frac{T_1}{T_2} \]

Where:
- \(χ_1\) is the susceptibility at temperature \(T_1\)
- \(χ_2\) is the susceptibility at temperature \(T_2\)

### Step 1: Convert the given temperature to Kelvin
The given temperature \(T_1\) is \(27^\circ C\). To convert this to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273.15 \]

Calculating this gives:

\[ T_1 = 27 + 273.15 = 300.15 \approx 300 \text{ K} \]

### Step 2: Write down the given values
From the problem, we have:
- \(χ_1 = 1.2 \times 10^{-5}\)
- \(χ_2 = 1.44 \times 10^{-5}\)
- \(T_1 = 300 \text{ K}\)

### Step 3: Use the susceptibility-temperature relationship
Using the relationship mentioned earlier, we can rearrange it to find \(T_2\):

\[ T_2 = T_1 \times \frac{χ_1}{χ_2} \]

### Step 4: Substitute the known values into the equation
Substituting the values we have:

\[ T_2 = 300 \times \frac{1.2 \times 10^{-5}}{1.44 \times 10^{-5}} \]

### Step 5: Simplify the fraction
The \(10^{-5}\) cancels out:

\[ T_2 = 300 \times \frac{1.2}{1.44} \]

Calculating the fraction:

\[ \frac{1.2}{1.44} = \frac{12}{14.4} = \frac{5}{6} \approx 0.8333 \]

### Step 6: Calculate \(T_2\)
Now substituting back:

\[ T_2 = 300 \times 0.8333 \approx 250 \text{ K} \]

### Step 7: Find \(T/10\)
Now, we need to find \(T_2/10\):

\[ \frac{T_2}{10} = \frac{250}{10} = 25 \]

### Final Answer
Thus, the value of \(T/10\) is:

\[ \boxed{25} \]