The SI unit for the coefficient of cubical expansion is

Options

A. `.^@C`
B. `"per".^@C`
C. `"cm"//.^@C`
D. none of these

Answer

To find the SI unit for the coefficient of cubical expansion, we can follow these steps:

### Step 1: Understand the Concept
The coefficient of cubical expansion (β) is defined as the fractional change in volume per unit change in temperature. It indicates how much a material expands when it is heated.

### Step 2: Mathematical Expression
The mathematical expression for the coefficient of cubical expansion is given by:
\[ \beta = \frac{\Delta V / V}{\Delta T} \]
Where:
- \(\Delta V\) = Change in volume
- \(V\) = Original volume
- \(\Delta T\) = Change in temperature

### Step 3: Analyze the Units
From the expression, we can see that:
- The term \(\Delta V / V\) is dimensionless (it is a ratio of two volumes).
- The change in temperature \(\Delta T\) is measured in degrees (Celsius or Kelvin).

### Step 4: Determine the SI Unit
Since \(\Delta V / V\) is dimensionless, the unit of the coefficient of cubical expansion will be the inverse of the unit of temperature change. Therefore, the SI unit for the coefficient of cubical expansion is:
\[ \text{per degree Celsius} \quad \text{or} \quad \text{°C}^{-1} \]

### Final Answer
The SI unit for the coefficient of cubical expansion is \( \text{°C}^{-1} \).

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