The dimensional forumla for thermal resistance is

Options

A. `[ML^2T^(-3) K^(-1)]`
B. `[ML^2 T^(-2) A^(-1)]`
C. `[M^(-1) L^(-2) T^3 K]`
D. `[ML^2 T^(-3) K^(-2)]`

Explanation

To find the dimensional formula for thermal resistance, we start with the relationship that defines thermal resistance:

1. **Understanding Thermal Resistance**:
Thermal resistance (R) is defined as the temperature difference (ΔT) divided by the rate of heat flow (Q). Mathematically, this can be expressed as:
\[ R = \frac{\Delta T}{Q} \]

2. **Identifying the Dimensions**:
- **Temperature Difference (ΔT)**: The dimension of temperature is represented as [K] (Kelvin).
- **Rate of Heat Flow (Q)**: The rate of heat flow can be understood as energy per unit time. The dimension of energy is given by the formula:
\[ [E] = [M][L^2][T^{-2}] \]
where [M] is mass, [L] is length, and [T] is time. Therefore, the dimension of heat flow per unit time (Q) is:
\[ [Q] = \frac{[E]}{[T]} = \frac{[M][L^2][T^{-2}]}{[T]} = [M][L^2][T^{-3}] \]

3. **Combining the Dimensions**:
Now, substituting the dimensions of ΔT and Q into the formula for thermal resistance:
\[ R = \frac{[K]}{[M][L^2][T^{-3}]} \]
This can be rewritten as:
\[ R = [K][M^{-1}][L^{-2}][T^{3}] \]

4. **Final Dimensional Formula**:
Therefore, the dimensional formula for thermal resistance is:
\[ R = [M^{-1}][L^{-2}][K][T^{3}] \]

Thus, the final answer is:
\[ \text{Dimensional Formula of Thermal Resistance} = M^{-1}L^{-2}K^{1}T^{3} \]