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 problem of identifying which plot does not correctly describe the relation between various thermodynamic quantities for a diatomic ideal gas in a closed system, we can follow these steps:

### Step 1: Understand the Thermodynamic Quantities
- **Internal Energy (U)**: For an ideal gas, the change in internal energy (dU) is related to the heat capacity at constant volume (Cv) and the change in temperature (dT) by the equation:
\[ dU = C_v dT \]
- **Heat Capacities**:
- \(C_v\) is the heat capacity at constant volume.
- \(C_p\) is the heat capacity at constant pressure.

### Step 2: Analyze the Given Plots
- We have four plots to analyze. We need to check the relationships depicted in each plot against the known thermodynamic equations.

### Step 3: Evaluate Each Plot
- **Plot 1 and Plot 2**: Both plots are likely representing the relationship \(dU = C_v dT\). Since this is a direct relationship, these plots are correct.

- **Plot 3**: This plot is said to show a relationship between \(C_p\) and pressure (P). However, \(C_p\) is independent of pressure for an ideal gas. Thus, if the plot shows a direct relationship (like a straight line), it is incorrect.

- **Plot 4**: This plot needs to be checked against the known relationships, but since we have already identified Plot 3 as incorrect, we can conclude that Plot 4 is likely correct unless explicitly stated otherwise.

### Step 4: Conclusion
- Based on the analysis, the plot that does not correctly describe the relationship is **Plot 3**. Therefore, the answer to the question is:
\[ \text{Option C} \]