The limiting value of the ratio of pressures of a gas at the steam point and at the triple point of water when the gas is kept at constant volume is found to be \(1.365954\). What is the ideal-gas temperature of the steam point to six significant figures?

The concept of the triple point is a fundamental one in thermodynamics and physical chemistry. The triple point of a substance is the unique condition under which the three phases of matter—solid, liquid, and gas—coexist in thermodynamic equilibrium.
For water, the triple point is particularly important. It occurs at a specific temperature and pressure: exactly 273.16 Kelvin (0.01°C) and a pressure of about 611.657 pascals.
Understanding the triple point helps in establishing temperature scales and serves as a reference point for defining the Kelvin, the base unit of temperature in the International System of Units (SI).

The steam point refers to the temperature at which water boils under standard atmospheric pressure—normally taken as 100°C or 373.15 Kelvin. This is an important reference point in both the Celsius and Kelvin temperature scales.
At the steam point, water transitions from the liquid phase to the gaseous phase, known as steam. Like the triple point, the steam point is used to calibrate thermometers. It's also significant in various applications, from cooking to industrial processes.
In the context of the ideal gas law, knowing the steam point allows scientists to explore the relationship between pressure, volume, and temperature in gases.

The temperature ratio, often used in thermodynamics, is the ratio of temperatures at different conditions. According to the ideal gas law, the ratio of pressures of a gas at constant volume is directly proportional to the ratio of their absolute temperatures.
Mathematically, this relationship can be expressed as: \[\frac{\frac{P_1}{P_2}}{\frac{T_1}{T_2}} = 1\]
In the given exercise, we deal with the ratio of pressures at the steam point and the triple point. Since the gas was kept at a constant volume, this ratio equals the ratio of their absolute temperatures.
So, understanding this proportion allows us to find unknown parameters like the ideal-gas temperature of the steam point, using known values such as the triple point temperature.