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The dimensional formula for entropy is...

The dimensional formula for entropy is

A

`[MLT^(-2)K^(-1)]`

B

`[ML^2T^(-2)]`

C

`[ML^2T^(-2)K^(-1)]`

D

`[ML^(-2)T^(-2)K^(-1)]`

Text Solution

AI Generated Solution

The correct Answer is:
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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