How To Calculate Boiling Point Of Water At Different Pressures

Boiling Point Equation:

\[ T_b = \frac{1}{\frac{1}{T_0} - \frac{R}{\Delta H_{vap}} \ln \left( \frac{P}{P_0} \right)} \]

Boiling Point (T_b):

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1. What is the Boiling Point Equation?

The boiling point equation calculates the boiling temperature of water at different pressures using the Clausius-Clapeyron relation. It shows how boiling point changes with atmospheric pressure variations.

2. How Does the Calculator Work?

The calculator uses the boiling point equation:

\[ T_b = \frac{1}{\frac{1}{T_0} - \frac{R}{\Delta H_{vap}} \ln \left( \frac{P}{P_0} \right)} \]

Where:

\( T_b \) — Boiling point (K)
\( T_0 \) — Standard boiling point of water (373.15 K)
\( R \) — Gas constant (8.314 J/mol·K)
\( \Delta H_{vap} \) — Enthalpy of vaporization of water (40660 J/mol)
\( P \) — Pressure (Pa)
\( P_0 \) — Standard pressure (101325 Pa)

Explanation: The equation demonstrates the inverse relationship between pressure and boiling point - lower pressure results in lower boiling temperature.

3. Importance of Boiling Point Calculation

Details: Understanding boiling point variations is crucial for high-altitude cooking, industrial processes, meteorological studies, and chemical engineering applications where pressure conditions differ from standard atmospheric pressure.

4. Using the Calculator

Tips: Enter pressure in Pascals (Pa). The calculator will compute the corresponding boiling point of water in Kelvin. Pressure must be a positive value.

5. Frequently Asked Questions (FAQ)

Q1: Why does boiling point change with pressure?
A: Boiling occurs when vapor pressure equals atmospheric pressure. Lower atmospheric pressure means water molecules need less energy to escape, thus boiling at lower temperatures.

Q2: What is the boiling point at high altitudes?
A: At higher altitudes where pressure is lower, water boils at temperatures below 100°C. For example, at 3000m altitude, water boils at approximately 90°C.

Q3: How accurate is this equation?
A: The equation provides good approximations for most practical purposes, though very precise measurements might require more complex models accounting for non-ideal behavior.

Q4: Can this be used for other liquids?
A: The same principle applies, but different liquids have different \( T_0 \), \( \Delta H_{vap} \), and \( P_0 \) values that must be used in the equation.

Q5: What are typical pressure values?
A: Standard atmospheric pressure is 101325 Pa. High altitude areas might have pressures around 70000-90000 Pa, while pressure cookers operate at 150000-200000 Pa.