To understand the difference in pressures between the two constant-volume gas thermometers using nitrogen and helium, we need to consider how the properties of the gases affect their behavior under the same temperature conditions. Both thermometers are set to a pressure of 100 cm Hg at a constant volume, but the key lies in the molecular characteristics of nitrogen and helium.

Gas Properties and Behavior

When gases are heated, their pressure increases if the volume remains constant. This relationship is described by Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature (in Kelvin). However, the rate at which different gases respond to temperature changes can vary significantly due to their molecular weights and specific heat capacities.

Molecular Weight Considerations

Nitrogen (N₂) has a molecular weight of about 28 g/mol, while helium (He) has a much lower molecular weight of approximately 4 g/mol. This difference plays a crucial role in how each gas behaves when heated:

• Helium: Being lighter, helium molecules move faster at a given temperature compared to nitrogen molecules. This increased kinetic energy translates to a higher pressure in the same volume when heated.
• Nitrogen: The heavier nitrogen molecules have a slower average speed at the same temperature, resulting in a lower pressure compared to helium.

Calculating the Pressure Difference

At the boiling point of water (100°C or 373 K), both gases will exert pressure according to their respective molecular behaviors. Since both thermometers are initially set to the same pressure of 100 cm Hg, we can analyze how the pressures will differ at this temperature.

Using the ideal gas law, we can express the pressure of each gas as:

P = (nRT)/V

Where:

• P = pressure
• n = number of moles of gas
• R = ideal gas constant
• T = absolute temperature in Kelvin
• V = volume

Since the volume is constant and the number of moles is the same for both gases, the pressure will depend on the temperature and the specific gas constant (R) for each gas. Helium, with its lower molecular weight, will have a higher specific gas constant compared to nitrogen, leading to a greater increase in pressure at the same temperature.

Conclusion on Pressure Comparison

At the boiling point of water, the pressure in the helium thermometer will be higher than that in the nitrogen thermometer. This is due to the faster-moving helium molecules generating more pressure than the slower-moving nitrogen molecules under the same thermal conditions.

In summary, when both thermometers are placed in a boiling water bath, the pressure in the helium thermometer will exceed that in the nitrogen thermometer, illustrating the impact of molecular weight and gas properties on pressure behavior in thermodynamic systems.