Choose the wrong options

Options

A. Translational kinetic energy of all ideal gases at same temperature is same.
B. In one degree of freedom all ideal gases has interal energy = `(1)/(2) R T`
C. Translational degree of freedom of all ideal gases is three
D. Translational kinetic energy of one mole of all ideal gases is `(3)/(2) R T`

Answer

To solve the question of choosing the wrong options regarding the translational kinetic energy and internal energy of ideal gases, we will analyze the statements one by one.

### Step-by-Step Solution:

1. **Understanding Translational Kinetic Energy**:
- The translational kinetic energy of an ideal gas is given by the formula:
\[ KE = \frac{F}{2} RT \]
where \( F \) is the number of degrees of freedom, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

2. **Degrees of Freedom**:
- For ideal gases, the degrees of freedom for translational motion is 3 (x, y, z directions). Therefore, the translational kinetic energy for one mole of an ideal gas is:
\[ KE = \frac{3}{2} RT \]
- This means that the translational kinetic energy of all ideal gases at the same temperature is indeed the same, which makes this statement **true**.

3. **Internal Energy of Ideal Gases**:
- The internal energy \( U \) of an ideal gas is given by:
\[ U = \frac{F}{2} RT \]
- For one degree of freedom, the internal energy would be:
\[ U = \frac{1}{2} RT \]
- However, the statement in the question claims that for one degree of freedom, the internal energy is \( \frac{1}{2} RT \) for all ideal gases, which is misleading. The correct expression for one molecule in one degree of freedom is:
\[ U = \frac{1}{2} k T \]
- Therefore, the statement regarding the internal energy being \( \frac{1}{2} RT \) for one degree of freedom is **false**.

4. **Conclusion**:
- Based on the analysis, the wrong option is the one that states "in one degree of freedom, all ideal gases' internal energy is equal to \( \frac{1}{2} RT \)". This is incorrect because the correct expression should involve the Boltzmann constant \( k \) for a single molecule and not \( R \) for one mole.

### Final Answer:
The wrong option is **Option B**.

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