Boiling Point Calculator

This calculator relies on the Clausius-Clapeyron relation, a fundamental thermodynamic equation describing the phase boundary between a liquid and its vapor. The primary mathematical formulation used to find a new temperature (T2) at a target pressure (press2), given an initial temperature (T1), pressure (press1), and the substance's latent heat of vaporization ($\Delta H_{vap}$), is expressed as:

1 / T2 = (1 / T1) + [ ln(press1 / press2) * R ] / \Delta H_{vap}

Where R is the universal gas constant (8.31446 J/(mol*K)), temperatures are measured in Kelvin, and pressures share matching units. This relationship demonstrates that as external pressure drops, less thermal energy is required for vapor molecules to escape into the gas phase, thereby lowering the boiling point.

Let us calculate the boiling point of ethanol when the ambient pressure is reduced from a standard 101.3 kPa down to a vacuum of 50 kPa. Suppose the normal boiling point of ethanol at standard pressure (T1) is 351.5 Kelvin, and its latent heat of vaporization is approximately 38,560 J/mol.

Step 1: Input the known baseline values: T1 = 351.5 K, press1 = 101.3 kPa, press2 = 50 kPa, and latent heat = 38,560 J/mol.

Step 2: Calculate the natural logarithm of the pressure ratio: ln(101.3 / 50) = ln(2.026) ≈ 0.706.

Step 3: Multiply by the gas constant and divide by the latent heat: (0.706 * 8.31446) / 38560 ≈ 0.000152.

Step 4: Add this result to the inverse of the initial temperature: (1 / 351.5) + 0.000152 ≈ 0.002845 + 0.000152 = 0.002997.

Step 5: Invert the final sum to find T2: 1 / 0.002997 ≈ 333.6 Kelvin (or roughly 60.5°C). Thus, lowering the pressure significantly reduces the temperature required to boil ethanol.

Always ensure your pressure values use identical units (such as kilopascals, atmospheres, or torrs) so that the ratio inside the natural logarithm cancels out correctly. Keep in mind that temperatures must always be converted to absolute scales like Kelvin to prevent mathematical anomalies. Furthermore, remember that latent heat of vaporization can vary slightly across extreme temperature ranges, so this calculation yields the highest accuracy when the target pressure is relatively close to your baseline reference point.