The gas constant R represents work done

Options

A. per kelvin per mole
B. per degree absolute
C. per degree per mole
D. per mole

Answer

To solve the question regarding what the gas constant \( R \) represents, we can follow these steps:

### Step 1: Understand the Definition of the Gas Constant
The gas constant \( R \) is a fundamental constant in thermodynamics and is used in various equations, including the ideal gas law, which is expressed as:
\[ PV = nRT \]
where:
- \( P \) = pressure,
- \( V \) = volume,
- \( n \) = number of moles,
- \( T \) = temperature in Kelvin.

### Step 2: Identify the Units of the Gas Constant
The value of the gas constant \( R \) is commonly given as:
\[ R = 8.314 \, \text{J/(mol·K)} \]
This indicates that the units of \( R \) are joules per mole per Kelvin.

### Step 3: Interpret the Meaning of the Units
The units of \( R \) can be interpreted as the amount of energy (work done) per mole of substance per unit change in temperature. Therefore, it represents the energy associated with the movement of gas particles in relation to temperature changes.

### Step 4: Analyze the Options
Given the context of the question, we need to determine which option correctly describes \( R \) as the work done per Kelvin per mole. Since \( R \) is associated with energy (in joules), we can conclude that it indeed represents work done in relation to temperature and the number of moles.

### Conclusion
Based on the analysis, the correct interpretation is that the gas constant \( R \) represents work done per Kelvin per mole.

### Final Answer
The gas constant \( R \) represents work done per Kelvin per mole.

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