Which has maximum internal energy at `290K` ?

Options

A. Neon gas
B. Nitrogen gas
C. Ozone gas
D. Equal for all

Explanation

To determine which gas has the maximum internal energy at 290 K, we can use the formula for the internal energy of an ideal gas:

\[ U = \frac{f}{2} nRT \]

Where:
- \( U \) = internal energy
- \( f \) = degrees of freedom of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (approximately \( 8.314 \, \text{J/(mol K)} \))
- \( T \) = temperature in Kelvin

### Step 1: Identify the Degrees of Freedom for Each Gas
1. **Neon (Ne)**: Neon is a monoatomic gas, which has 3 degrees of freedom (f = 3).
2. **Nitrogen (N₂)**: Nitrogen is a diatomic gas and has 5 degrees of freedom (f = 5).
3. **Ozone (O₃)**: Ozone is a triatomic gas and has 6 degrees of freedom (f = 6).

### Step 2: Analyze the Internal Energy Formula
Since the temperature (T), the gas constant (R), and the number of moles (n) are the same for all gases at 290 K, the internal energy will depend solely on the degrees of freedom (f).

### Step 3: Compare the Internal Energies
- For Neon:
\[ U_{Ne} = \frac{3}{2} nRT \]

- For Nitrogen:
\[ U_{N_2} = \frac{5}{2} nRT \]

- For Ozone:
\[ U_{O_3} = \frac{6}{2} nRT \]

### Step 4: Determine Which Gas Has the Maximum Internal Energy
From the calculations:
- Neon has the lowest internal energy due to the lowest degrees of freedom (f = 3).
- Nitrogen has a higher internal energy than Neon (f = 5).
- Ozone has the highest internal energy due to the highest degrees of freedom (f = 6).

### Conclusion
Thus, the gas with the maximum internal energy at 290 K is **Ozone (O₃)**.

### Final Answer
**C. Ozone (O₃)**

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