The gases carbon-monoxide (CO) and nitrogen at the same temperature have kinetic energies `E_(1)` and `E_(2)` respectively. Then

Options

A. `E_(1)=E_(2)`
B. `E_(1) gt E_(2)`
C. `E_(1) lt E_(2)`
D. None of these

Explanation

To solve the problem regarding the kinetic energies of carbon monoxide (CO) and nitrogen (N₂) at the same temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Energy of Gases**:
The kinetic energy (KE) of a gas molecule is related to its temperature. For a diatomic gas, the average kinetic energy per molecule can be expressed using the formula:
\[ KE = \frac{f}{2} k T \]
where \( f \) is the degrees of freedom, \( k \) is the Boltzmann constant, and \( T \) is the temperature.

2. **Degrees of Freedom**:
Both carbon monoxide (CO) and nitrogen (N₂) are diatomic gases. For diatomic gases, the degrees of freedom \( f \) is typically 5 (3 translational and 2 rotational).

3. **Kinetic Energy Expressions**:
For carbon monoxide (CO), the kinetic energy \( E_1 \) can be written as:
\[ E_1 = \frac{5}{2} k T \]
For nitrogen (N₂), the kinetic energy \( E_2 \) can be expressed similarly:
\[ E_2 = \frac{5}{2} k T \]

4. **Same Temperature Condition**:
Since it is given that both gases are at the same temperature, we can denote this common temperature as \( T \). Thus, we have:
\[ E_1 = \frac{5}{2} k T \quad \text{and} \quad E_2 = \frac{5}{2} k T \]

5. **Comparison of Kinetic Energies**:
Since both expressions for \( E_1 \) and \( E_2 \) are identical (as they depend on the same temperature \( T \)), we can conclude:
\[ E_1 = E_2 \]

6. **Conclusion**:
Therefore, the correct answer is that the kinetic energies of carbon monoxide and nitrogen at the same temperature are equal, which corresponds to option 1.

### Final Answer:
**E1 is equal to E2.** (Option 1)