Find SI units of thermal resistance.

Explanation

To find the SI units of thermal resistance, we can follow these steps:

### Step 1: Understand the relationship
Thermal resistance (R) can be defined using the formula derived from Fourier's law of heat conduction. The formula for thermal resistance is given by:

\[ R = \frac{T_1 - T_2}{Q} \]

where \( T_1 \) and \( T_2 \) are temperatures, and \( Q \) is the heat transfer rate.

### Step 2: Rearranging the formula
From the formula, we can express \( Q \) in terms of thermal resistance:

\[ Q = \frac{T_1 - T_2}{R} \]

### Step 3: Substitute the expression for heat transfer
From Fourier's law, the heat transfer rate \( Q \) for a rectangular slab can be expressed as:

\[ Q = -k \cdot A \cdot \frac{dT}{dx} \]

For a temperature difference \( \Delta T \) across a thickness \( L \):

\[ Q = \frac{k \cdot A \cdot (T_1 - T_2)}{L} \]

### Step 4: Relate thermal resistance to the parameters
Now, substituting this expression for \( Q \) into the thermal resistance formula gives:

\[ R = \frac{L}{k \cdot A} \]

### Step 5: Identify the units
Now we need to find the SI units of each component in the equation:

- Length \( L \) has units of meters (m).
- Thermal conductivity \( k \) has units of watts per meter Kelvin (W/(m·K)).
- Area \( A \) has units of square meters (m²).

### Step 6: Substitute the units into the thermal resistance formula
Substituting the units into the thermal resistance formula:

\[ R = \frac{\text{meters (m)}}{\text{(watts (W) / (meters (m) \cdot Kelvin (K)))} \cdot \text{(square meters (m²))}} \]

This simplifies to:

\[ R = \frac{m}{\frac{W}{m \cdot K} \cdot m^2} \]

### Step 7: Simplifying the units
This can be simplified further:

\[ R = \frac{m^3 \cdot K}{W} \]

### Step 8: Final simplification
Since \( m^3 \) cancels out with one \( m \) in the denominator:

\[ R = \frac{K}{W} \]

### Conclusion
Thus, the SI units of thermal resistance \( R \) are:

\[ \text{Kelvin per watt (K/W)} \]

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