Assuming ideal gas Cvm will be temperature independent forA)o3B)N2C)Co2D)He

To determine which gas has a constant molar heat capacity at constant volume (Cvm) that is temperature independent, we need to consider the nature of the gas and its molecular structure. In this case, we are looking at four different gases: O3 (ozone), N2 (nitrogen), CO2 (carbon dioxide), and He (helium).

Understanding Cvm and Its Dependence on Temperature

The molar heat capacity at constant volume, Cvm, is a measure of how much energy is required to raise the temperature of one mole of a substance by one degree Celsius while keeping the volume constant. For ideal gases, Cvm can vary with temperature, especially for polyatomic gases, due to the excitation of vibrational modes.

Analyzing Each Gas

• O3 (Ozone): Ozone is a triatomic molecule and has multiple vibrational modes. As temperature increases, these modes become excited, leading to a temperature-dependent Cvm.
• N2 (Nitrogen): Nitrogen is a diatomic molecule. While it has some vibrational modes, they are less significant compared to triatomic gases. However, Cvm can still vary slightly with temperature.
• CO2 (Carbon Dioxide): CO2 is a linear triatomic molecule. Similar to ozone, it has several vibrational modes that become active at higher temperatures, making Cvm temperature-dependent.
• He (Helium): Helium is a monatomic gas. Monatomic gases have no vibrational modes and only possess translational and rotational degrees of freedom. This means that Cvm remains constant with temperature changes.

Conclusion on Temperature Independence

Among the options provided, helium (He) is the gas for which Cvm is temperature independent. This is due to its simple atomic structure, which does not allow for vibrational excitations that would affect heat capacity. Therefore, the correct answer is He.

Why This Matters

Understanding the behavior of different gases under varying temperatures is crucial in fields like thermodynamics and physical chemistry. It helps in predicting how gases will behave in different conditions, which is essential for applications ranging from industrial processes to environmental science.