Which of the following statement is true?

Options

A. Absolute zero degree temperature is not zero enery temperature.
B. Two different gases at the same temperature pressure have equal root mean square velocities.
C. The rms speed of the molecules of different ideal gases, maintained at the same temperature are the same.
D. Given sample of 1cc of hydrogen and 1cc of oxygen both at N.T.P.,oxygen sample has a large number of molecules.

Answer

To determine which statement is true among the given options, let's analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** Absolute zero degree temperature is not zero energy temperature.

- At absolute zero (0 Kelvin), the kinetic energy of gas molecules approaches zero.
- However, according to quantum mechanics, particles still possess some potential energy due to their inherent quantum states.
- Therefore, while kinetic energy is zero, total energy (kinetic + potential) is not zero.

**Conclusion:** Statement A is true.

### Step 2: Analyze Statement B
**Statement B:** Two different gases at the same temperature and pressure have equal root mean square velocity.

- The root mean square (RMS) velocity is given by the formula:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the gas constant, \( T \) is the temperature, and \( M \) is the molar mass of the gas.
- For two different gases at the same temperature, their RMS velocities will depend on their molar masses. Since the molar masses are different, the RMS velocities will also be different.

**Conclusion:** Statement B is false.

### Step 3: Analyze Statement C
**Statement C:** The RMS speed of the molecules of different ideal gases maintained at the same temperature are the same.

- This statement is similar to Statement B and relies on the same formula for RMS velocity.
- Since different gases have different molar masses, their RMS speeds will not be the same even if the temperature is the same.

**Conclusion:** Statement C is false.

### Step 4: Analyze Statement D
**Statement D:** Given a sample of one cubic centimeter of hydrogen and one cubic centimeter of oxygen both at NTP, the oxygen sample has a larger number of molecules.

- According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules, regardless of the type of gas.
- Therefore, one cubic centimeter of hydrogen and one cubic centimeter of oxygen at the same conditions will have the same number of molecules.

**Conclusion:** Statement D is false.

### Final Conclusion
After analyzing all four statements, we find that only **Statement A** is true.