A constant-volume gas thermometer registers an absolute pressure corresponding to $325$ mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?

Verified step by step guidance

1. Understand the concept of a constant-volume gas thermometer: It measures temperature by the pressure of a gas at constant volume. The pressure is directly proportional to the temperature in Kelvin.
2. Recall the triple point of water: It is the temperature and pressure at which water can coexist in solid, liquid, and gas phases. The triple point temperature is 273.16 K.
3. Use the ideal gas law relation for constant volume: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), where \( P_1 \) and \( T_1 \) are the pressure and temperature at the triple point, and \( P_2 \) and \( T_2 \) are the pressure and temperature at the boiling point.
4. Identify the normal boiling point of water: The temperature at which water boils under standard atmospheric pressure is 100°C, which is 373.15 K in Kelvin.
5. Substitute the known values into the equation: \( P_1 = 325 \) mmHg, \( T_1 = 273.16 \) K, and \( T_2 = 373.15 \) K. Solve for \( P_2 \) using \( P_2 = P_1 \times \frac{T_2}{T_1} \).

Key Concepts

Triple Point of Water

The triple point of water is the unique temperature and pressure at which water can coexist in equilibrium in its solid, liquid, and gaseous states. It is precisely defined as 0.01°C and 611.657 pascals. Understanding this concept is crucial because it provides a reference point for calibrating thermometers, including constant-volume gas thermometers.

Constant-Volume Gas Thermometer

A constant-volume gas thermometer measures temperature by observing the pressure of a gas at a fixed volume. The pressure changes proportionally with temperature, following the ideal gas law. This type of thermometer is highly accurate and is often used to define temperature scales, making it essential for understanding how pressure readings relate to temperature changes.

Normal Boiling Point of Water

The normal boiling point of water is the temperature at which water transitions from liquid to gas at standard atmospheric pressure (1 atm or 101325 pascals). It is 100°C. Knowing this point is important for determining the pressure reading of a constant-volume gas thermometer when it is in contact with boiling water, as the pressure will reflect the increased temperature compared to the triple point.