Which of the following statement is true

To determine the correct statement, let us analyze each of the options step-by-step:

1. Analyzing Option 1: "Absolute zero degree temperature is not zero energy temperature"
According to classical thermodynamics, at absolute zero temperature (0 K), the thermal motion of molecules ceases, and the classical kinetic energy becomes zero. However, according to quantum mechanics, particles possess a non-zero minimum energy even at absolute zero temperature (0 K). This is known as the zero-point energy, which arises due to the Heisenberg Uncertainty Principle. Since a particle cannot have both a precisely defined position and momentum, it cannot be completely at rest. Therefore, absolute zero degree temperature is not a state of zero energy. This statement is true.

2. Analyzing Option 2: "Two different gases at the same temperature pressure have equal root mean square velocities"
The root-mean-square (rms) velocity of a gas is given by the formula:
$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$
where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas. Since the root-mean-square velocity depends inversely on the square root of the molar mass ($M$), two different gases (with different molar masses) at the same temperature will have different rms velocities. Thus, this statement is false.

3. Analyzing Option 3: "The rms speed of the molecules of different ideal gases, maintained at the same temperature are the same"
As shown in the analysis of Option 2, the rms speed is inversely proportional to the square root of the molar mass ($v_{\text{rms}}\propto \frac{1}{\sqrt{M}}$). Therefore, different ideal gases at the same temperature will have different rms speeds depending on their molar masses. Thus, this statement is false.

4. Analyzing Option 4: "Given sample of 1cc of hydrogen and 1cc of oxygen both at N.T.P.; oxygen sample has a large number of molecules"
According to Avogadro's hypothesis, equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules. Since both the hydrogen and oxygen samples have a volume of 1 cc and are at N.T.P. (Normal Temperature and Pressure), they must contain the exact same number of molecules. Thus, this statement is false.

Therefore, the only true statement is that absolute zero degree temperature is not zero energy temperature.