The dimensions of thermal resistance are

Options

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

Answer

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

### Step 1: Understand the formula for thermal resistance
Thermal resistance (R) is defined as the ratio of the temperature difference (ΔT) to the rate of heat flow (Q). Mathematically, this can be expressed as:
\[ R = \frac{\Delta T}{Q} \]

### Step 2: Identify the dimensions of temperature difference (ΔT)
The dimension of temperature (T) is represented as:
\[ [\Delta T] = K \]
where K represents the dimension of temperature.

### Step 3: Identify the dimensions of the rate of heat flow (Q)
The rate of heat flow (Q) can be expressed in terms of mass (m), length (L), and time (T). The dimension of heat flow is:
\[ [Q] = \frac{M L^2}{T^2} \]
This represents the amount of heat transferred per unit time.

### Step 4: Substitute the dimensions into the thermal resistance formula
Now we can substitute the dimensions of ΔT and Q into the formula for thermal resistance:
\[ R = \frac{[\Delta T]}{[Q]} = \frac{K}{\frac{M L^2}{T^2}} \]

### Step 5: Simplify the expression
When we simplify this expression, we multiply by the reciprocal of the denominator:
\[ R = K \cdot \frac{T^2}{M L^2} \]
This can be rearranged to:
\[ R = \frac{K T^2}{M L^2} \]

### Step 6: Write the final dimensions of thermal resistance
Thus, the dimensions of thermal resistance (R) can be expressed as:
\[ [R] = M^{-1} L^{-2} K T^2 \]

### Final Answer
The dimensions of thermal resistance are:
\[ [R] = M^{-1} L^{-2} K T^2 \]

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