`He,N_(2)`, and `O_(3)` are expanded adiabatically and their expansion curves between `P` and `V` are plotted under silimar conditions. About the ratio of the slope, which one is not correct?

Options

A. The ratio of slopes of `P-V` curves for `He` and `O_(3) is 1.25`.
B. The ratio of slopes of `P-V` curves for `He` and `N_(2) is 1.20`.
C. The ratio of slopes of `P-V` curves for `N_(2)` and `O_(3) is 1.05`.
D. The slope of `He` is least steeper and for `O_(3)` is most steeper.

Explanation

To solve the problem regarding the adiabatic expansion of helium (He), nitrogen (N₂), and ozone (O₃), we need to analyze the slopes of their respective P-V curves based on the adiabatic process. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Adiabatic Process
The adiabatic process for an ideal gas is described by the equation:
\[ PV^\gamma = \text{constant} \]
where \( \gamma \) (gamma) is the adiabatic index, defined as:
\[ \gamma = \frac{C_p}{C_v} \]
where \( C_p \) is the heat capacity at constant pressure and \( C_v \) is the heat capacity at constant volume.
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