The unit of entropy is

Options

A. `JK ^(-1) mol ^(-1)`
B. `J mol^(-1)`
C. `J^(-1)K^(-1) mol^(-1)`
D. `JK mol^(-1)`

Answer

To determine the unit of entropy, we can follow these steps:

### Step 1: Understand the Definition of Entropy
Entropy (S) is a measure of the disorder or randomness in a system. It is defined in thermodynamics as the change in entropy (ΔS) being equal to the heat transferred (Q) in a reversible process divided by the temperature (T) at which the transfer occurs.

### Step 2: Write the Formula for Change in Entropy
The formula for change in entropy is given by:
\[ \Delta S = \frac{Q_{\text{reversible}}}{T} \]
Where:
- \( \Delta S \) = Change in entropy
- \( Q_{\text{reversible}} \) = Heat transferred in a reversible process
- \( T \) = Temperature in Kelvin

### Step 3: Identify the Units of Heat and Temperature
- The unit of heat (\( Q \)) is Joules (J).
- The unit of temperature (\( T \)) is Kelvin (K).

### Step 4: Substitute the Units into the Formula
Substituting the units into the formula for entropy gives:
\[ \Delta S = \frac{\text{Joules}}{\text{Kelvin}} \]
However, since heat is often expressed per mole in thermodynamics, we also consider the amount of substance in moles (mol). Therefore, we can express the heat transferred as:
\[ Q_{\text{reversible}} = \text{Joules per mole} = \text{J mol}^{-1} \]

### Step 5: Combine the Units
Now, substituting this into the entropy formula:
\[ \Delta S = \frac{\text{J mol}^{-1}}{\text{K}} = \text{J mol}^{-1} \text{K}^{-1} \]
Thus, the unit of entropy can be expressed as:
\[ \text{J K}^{-1} \text{mol}^{-1} \]

### Final Answer
The unit of entropy is:
\[ \text{J K}^{-1} \text{mol}^{-1} \]

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