A non linear triatomic gas at temperature T and has 1 mole of molecule...
Total Energy of a Nonlinear Triatomic Gas
The total energy of a gas can be divided into different modes of motion, such as translational, rotational, and vibrational. In the case of a nonlinear triatomic gas, the vibrational modes of motion can be active or inactive depending on the temperature.
1. Inactive Vibrational Modes
When the vibrational modes of the gas are not active, the total energy of the gas is given by the sum of the translational and rotational energies. The translational energy is related to the kinetic energy of the gas molecules due to their linear motion, while the rotational energy is related to the kinetic energy of the gas molecules due to their rotational motion.
2. Active Vibrational Modes
When the vibrational modes of the gas are active, the total energy of the gas also includes the energy associated with the vibrational motion. Vibrational motion involves the oscillation of the atoms/molecules around their equilibrium positions, and this motion requires additional energy.
3. Ratio of Total Energy
To determine the ratio of the total energy when the vibrational modes are not active to when they are active, we need to compare the energy contributions from the translational and rotational motion to the energy contribution from the vibrational motion.
At low temperatures, the vibrational modes are generally not active, and the energy contribution from the vibrational motion is negligible compared to the translational and rotational energies. As the temperature increases, the vibrational modes become more active, and the energy contribution from the vibrational motion becomes significant.
Thus, the ratio of the total energy when the vibrational modes are not active to when they are active decreases as the temperature increases. At very high temperatures, the vibrational energy contributions dominate, and the ratio approaches unity.
In summary, the ratio of the total energy of a non-linear triatomic gas when its vibrational modes are not active to when they are active depends on the temperature. At low temperatures, the ratio is close to zero, while at high temperatures, the ratio approaches unity.