A Clausius–Clapeyron calculator is a web-based tool that uses the Clausius–Clapeyron relation to compute vapor pressures, temperatures, or the enthalpy of vaporization (ΔH₍vap₎) from one or more temperature–pressure data pairs, and to fit ΔH₍vap₎ by performing a linear regression of ln(P) against 1/T.

How to use the Clausius–Clapeyron Calculator

What this calculator does

This interactive calculator implements the Clausius–Clapeyron equation:ln⁡(P2P1)=−ΔHvapR(1T2−1T1)ln(P1​P2​​)=−RΔHvap​​(T2​1​−T1​1​)

It supports:

• Direct computations (compute P₂ given P₁, T₁, T₂ and ΔH; compute T₂ given P₂; compute ΔH from two P–T points).
• Fitting ΔH using multiple measured (T, P) pairs by plotting ln(P) vs 1/T and finding the best-fit line; slope → ΔH.
• A Plotly.js plot of ln(P) versus 1/T with scatter and regression line, so you can visually inspect data quality and fit.

This tool is designed to be embedded into a WordPress custom code block between sidebars. It uses a white background, a responsive width capped at 760px (typical content width), and modern, minimal styling suited to most themes.

Inputs and units

Single-calculation mode

• P₁, P₂: Enter pressures (supported units: kPa, bar, Pa, atm). Internally, all pressures convert to Pascals for calculation.
• T₁, T₂: Enter temperatures in °C or K. The calculator performs conversions to Kelvin where needed.
• ΔH₍vap₎: Enter the enthalpy of vaporization in J/mol or kJ/mol. The tool uses R=8.314462618 J\cdotpmol−1K−1R=8.314462618 J\cdotpmol−1K−1.

Choose the calculation mode from the dropdown:

• Compute P₂ (given P₁, T₁, T₂, ΔH)
• Compute T₂ (given P₁, T₁, P₂, ΔH)
• Compute ΔH (given P₁, T₁, P₂, T₂)

Fit mode (multiple data points)

If you have several experimental T–P pairs, add them to the table. Conventionally enter T in °C and P in kPa (the tool converts to Kelvin and Pascals internally). Click Fit ΔH from table to:

• Convert the data into x = 1/T (1/K) and y = ln(P) (natural log).
• Perform a least-squares linear fit to obtain slope (m) and intercept (b).
• Compute ΔH from the slope: ΔHvap=−slope×RΔHvap​=−slope×R.
• Display the fitted ΔH in kJ/mol and J/mol, and render a Plotly.js chart showing data points and the regression line.

Step-by-step usage

1. Embed the code: Copy the single-file HTML/JS into WordPress using a Custom HTML block (or a child theme template) in the location between your sidebars. The contained stylesheet ensures it fits typical content widths and looks native.
2. Choose a mode from the Mode dropdown.
3. Enter input values: Ensure units are correct. For single-calculation modes, fill P and T fields and ΔH if needed.
4. Click Calculate. Results appear immediately in the output panel.
5. For fitting: add rows of T and P pairs. Prefer at least three points for a robust fit but two will produce a slope as well. Click Fit ΔH from table to see the plot and fitted ΔH.
6. Inspect plot and result: The plot shows ln(P) vs 1/T. A straight-line fit indicates the Clausius–Clapeyron assumptions are reasonably satisfied over your temperature range.

Best practices and tips

• Units: Always double-check units. The tool accepts multiple pressure and temperature units; convert if needed before analysis.
• Temperature range: The Clausius–Clapeyron linearization (assuming ΔH is constant) works best over modest temperature ranges where ΔH₍vap₎ doesn’t change much.
• Data quality: Outliers in your (T,P) set will distort slope and ΔH. Use the Plotly plot to spot outliers.
• Precision: Enter measured pressures and temperatures with appropriate precision; the calculator will display ΔH in both J/mol and kJ/mol.
• Interpretation: Remember the fit provides an empirical ΔH assuming ideal behavior and negligible heat capacity differences between phases. For rigorous thermodynamics at wide temperature ranges, consider temperature-dependent ΔH models.

Technical notes (for developers)

• The tool uses Plotly.js for plotting and a simple least-squares routine implemented in JavaScript for linear regression.
• It uses a responsive container (max-width 760px), white background, and light box-shadow to match typical WordPress content areas between sidebars.
• The code is a single file (HTML + CSS + JS) so you can paste directly into an HTML block, or save as a partial template in a child theme.

Disclaimer

This calculator is provided for educational and illustrative purposes only. Results are approximate and depend on the accuracy of the input data and the validity of the Clausius–Clapeyron assumptions (e.g., constant ΔH over the temperature range). For critical engineering or safety-related calculations consult primary literature, validated databases, or a qualified engineer/chemist.

FAQ

Q1: What inputs are required to compute ΔH using this tool?
A: To compute ΔH directly you need two pairs of (P₁, T₁) and (P₂, T₂) — pressures and temperatures. The calculator converts units internally and returns ΔH in J/mol and kJ/mol.

Q2: Why do we plot ln(P) vs 1/T?
A: Rearranging the Clausius–Clapeyron equation yields a linear relationship ln⁡P=−ΔH/R∗(1/T)+ClnP=−ΔH/R∗(1/T)+C. Plotting ln(P) vs 1/T gives a straight line whose slope is −ΔH/R−ΔH/R; thus slope → ΔH.

Q3: How many data points do I need to fit ΔH reliably?
A: At least two points will define a line, but 3–6 well-measured points across the temperature range give a more reliable least-squares estimate and allow you to detect outliers.

Q4: Can I use this tool for non-ideal systems?
A: The Clausius–Clapeyron relation assumes ideal behavior and constant ΔH over the temperature range. For strongly non-ideal systems or wide temperature ranges, the result is less reliable.

Q5: Is the result suitable for engineering design?
A: Treat outputs as approximations. For design or safety-critical work, use validated data sources and consult domain experts.