For the equation `C_p - C_v` = R, the significance of R is

Options

A. Work done per mole per Kelvin
B. Heat absorbed per mole per Kelvin
C. Heat released per mole per Kelvin (
D. Work done per mole per degree celsius

Explanation

To understand the significance of R in the equation \( C_p - C_v = R \), we can break down the components of the equation step by step.

### Step 1: Understand the Terms
- \( C_p \) is the heat capacity at constant pressure.
- \( C_v \) is the heat capacity at constant volume.
- \( R \) is the gas constant.

### Step 2: Analyze the Equation
The equation \( C_p - C_v = R \) is derived from the first law of thermodynamics and relates to the behavior of ideal gases. It indicates that the difference between the heat capacities at constant pressure and constant volume is equal to the gas constant.

### Step 3: Significance of R
In the context of the equation:
- \( R \) signifies the amount of energy (or work) done per mole per unit change in temperature (Kelvin or degree Celsius).
- It represents the energy required to perform work when a gas expands at constant pressure.

### Step 4: Units of R
The units of \( R \) can be expressed as:
- Joules per mole per Kelvin (J/(mol·K))
- This indicates that \( R \) is a measure of energy per mole for a temperature change of one Kelvin.

### Step 5: Conclusion
Thus, the significance of \( R \) in the equation \( C_p - C_v = R \) is that it quantifies the work done per mole per Kelvin during the expansion of an ideal gas.

### Final Answer
The significance of \( R \) is that it represents the work done per mole per Kelvin.

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