for a diatomic ideal gas in a closed system , which of the following plots does not correctly describe the relation between various thermodynamic quantities ?

Options

A.
B.
C.
D.

Explanation

To solve the question regarding which plot does not correctly describe the relation between various thermodynamic quantities for a diatomic ideal gas in a closed system, we will analyze each of the given plots step by step.

### Step 1: Understand the Thermodynamic Quantities
- **Cp**: Heat capacity at constant pressure.
- **Cv**: Heat capacity at constant volume.
- **U**: Internal energy.
- **T**: Temperature.
- **P**: Pressure.
- **V**: Volume.

### Step 2: Analyze Each Plot
1. **Plot of Cp vs P**:
- For an ideal gas, the heat capacity at constant pressure (Cp) is generally considered to be constant for a given gas.
- Therefore, as pressure (P) increases, Cp should not increase.
- If the plot shows an increasing trend of Cp with P, this is incorrect.

2. **Plot of Cv vs V**:
- The heat capacity at constant volume (Cv) is also generally constant for an ideal gas.
- If this plot shows Cv remaining constant as volume (V) changes, this is correct.

3. **Plot of U vs T**:
- The internal energy (U) of an ideal gas is a function of temperature (T).
- For a diatomic ideal gas, U increases with an increase in T, which is correct.

4. **Plot of Cv vs T**:
- Cv typically increases with temperature for a diatomic gas due to additional degrees of freedom being activated as temperature rises.
- If this plot shows an increasing trend of Cv with T, this is also correct.

### Step 3: Identify the Incorrect Plot
- From the analysis, the plot of **Cp vs P** does not correctly describe the relationship, as it incorrectly suggests that Cp increases with pressure.

### Conclusion
The plot that does not correctly describe the relation between various thermodynamic quantities for a diatomic ideal gas in a closed system is the **Cp vs P plot**.

### Final Answer
The answer is the plot of **Cp vs P**.

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