Choose the wrong statement

Options

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

Answer

To solve the question "Choose the wrong statement," we will analyze each of the provided statements regarding the kinetic theory of gases and determine which one is incorrect.

### Step-by-Step Solution:

1. **Understanding the First Statement**:
- The first statement claims that the translational kinetic energy of all ideal gases at the same temperature is the same.
- According to the kinetic theory, the translational kinetic energy (E_k) for n moles of an ideal gas can be expressed as:
\[ E_k = \frac{3}{2} nRT \]
- Here, \( R \) is the universal gas constant, \( T \) is the temperature, and \( n \) is the number of moles. Since all variables are the same for ideal gases at the same temperature, this statement is **true**.

2. **Understanding the Second Statement**:
- The second statement asserts that in one degree of freedom, all ideal gases have internal energy equal to \( \frac{1}{2} RT \).
- The internal energy (U) of an ideal gas can be calculated using:
\[ U = \frac{f}{2} nRT \]
- For one degree of freedom (f = 1), the internal energy becomes:
\[ U = \frac{1}{2} nRT \]
- This statement is also **true**.

3. **Understanding the Third Statement**:
- The third statement claims that the translational kinetic energy of all ideal gases is 3.
- This is misleading. The correct expression for translational kinetic energy per mole is:
\[ E_k = \frac{3}{2} RT \]
- The statement incorrectly states that the kinetic energy itself is 3, which is not dimensionally correct. Therefore, this statement is **false**.

4. **Understanding the Fourth Statement**:
- The fourth statement reiterates that the translational kinetic energy of all ideal gases is \( \frac{3}{2} RT \).
- This is indeed the correct expression for the translational kinetic energy of an ideal gas per mole, making this statement **true**.

### Conclusion:
The wrong statement among the options provided is the third statement, which inaccurately claims that the translational kinetic energy of all ideal gases is 3.

### Final Answer:
The wrong statement is **Option 3**.

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