The dimensional formula for entropy is

Options

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

Answer

To find the dimensional formula for entropy, we can follow these steps:

### Step 1: Understand the Definition of Entropy
Entropy is defined as a measure of randomness or disorder in a system. It can also be expressed in terms of heat transfer and temperature.

### Step 2: Write the Formula for Entropy
Entropy (S) can be expressed as:
\[ S = \frac{Q}{T} \]
where:
- \( S \) is the entropy,
- \( Q \) is the heat transferred,
- \( T \) is the temperature.

### Step 3: Determine the Dimensional Formula for Heat (Q)
The dimensional formula for heat (Q) can be derived from the work-energy principle. Heat has the same dimensions as energy, which is given by:
\[ [Q] = [\text{Energy}] = [M L^2 T^{-2}] \]
where:
- \( M \) is mass,
- \( L \) is length,
- \( T \) is time.

### Step 4: Determine the Dimensional Formula for Temperature (T)
The dimensional formula for temperature is:
\[ [T] = [K] \]
where \( K \) represents the Kelvin unit of temperature.

### Step 5: Combine the Dimensional Formulas
Now, substituting the dimensional formulas for \( Q \) and \( T \) into the entropy formula:
\[ [S] = \frac{[Q]}{[T]} = \frac{[M L^2 T^{-2}]}{[K]} \]

### Step 6: Simplify the Dimensional Formula for Entropy
This gives us:
\[ [S] = [M L^2 T^{-2} K^{-1}] \]

### Conclusion
Thus, the dimensional formula for entropy is:
\[ [S] = [M L^2 T^{-2} K^{-1}] \]

### Final Answer
The dimensional formula for entropy is \( ML^2 T^{-2} K^{-1} \).

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