Question

A closed flask contains water in all its three states: solid, liquid and vapour at \(0^{\circ} \mathrm{C} .\) In this situation the average kinetic energy of the water molecule will be (1) The greater in the vapour state (2) The same in the three states (3) The greatest in the solid state (4) Greater in the liquid than in the vapour state

Short answer

The same in the three states

Step-by-step solution

- Understanding Kinetic Energy

The average kinetic energy of molecules in a substance is related to the temperature of the substance. At a given temperature, the average kinetic energy depends only on the temperature and not the phase of the substance.

- Analyzing the System

The flask contains water in all three states (solid, liquid, and vapour) at a constant temperature of 0°C. This suggests that the temperature is uniform throughout the entire system.

- Average Kinetic Energy

Since the kinetic energy depends only on temperature for a given substance, and all parts of the system are at 0°C, the average kinetic energy of water molecules in the system will be the same irrespective of the phase (solid, liquid, vapour).

- Conclusion

From the previous steps, it follows that the average kinetic energy of the water molecules will be the same in all three states at the given temperature of 0°C.

Key concepts

Phases of Water

Water exists in three distinct phases: solid (ice), liquid (water), and gas (vapor). Each phase has unique properties because of the strength of the intermolecular forces holding the molecules together.
In the solid phase (ice), water molecules are held in a rigid structure with minimal movement. This gives ice its solid shape and structure.
In the liquid phase, water molecules are more loosely packed. They can slide past one another, allowing water to flow and take the shape of its container.
In the gas phase (vapor), water molecules are much farther apart and move freely, filling the entire volume of their container. Understanding these phases is crucial when discussing kinetic energy and temperature’s impact on water.

Average Kinetic Energy

The average kinetic energy of molecules is directly related to the temperature of the substance. At any given temperature, the average kinetic energy (\text{KE}_{avg}\text{)} can be expressed using the formula:
\[ \text{KE}_{avg} = \frac{3}{2} k_B T \]
where \(k_B\) is the Boltzmann constant, and \(T\) is the temperature in Kelvin. Thus, if the temperature is the same, molecules in different phases have the same average kinetic energy. This is why, in the exercise, the water molecules in solid, liquid, and vapor phases at 0°C have the same average kinetic energy, despite being in different phases.

Temperature Dependence

Temperature plays a critical role in determining the kinetic energy of molecules. As temperature increases, the kinetic energy of molecules also rises, causing molecules to move faster. At higher temperatures, water molecules gain enough energy to overcome the forces holding them in a specific phase and transition to another phase (e.g., ice melting to water or water boiling to vapor). Conversely, lowering the temperature reduces kinetic energy, slowing down molecular movement and potentially causing phase transitions such as water freezing into ice.
The relationship between temperature and kinetic energy is foundational in understanding physical changes and thermodynamic processes in substances like water.