Heat Calorimetry Calculator

• Sensible heat: Q = m·c·ΔT, where ΔT = T₂ − T₁.
• Latent heat: Q = m·L, where L is the latent heat of fusion/vaporization.
• Mixing calorimetry: energy lost by hot equals energy gained by cold plus calorimeter, optionally adjusted by heat-loss fraction f.

1. Select a Calculation Mode matching your experiment.
2. Choose consistent mass and temperature units for your measurements.
3. Enter known quantities. If you want an unknown, pick it in Solve For.
4. Click Calculate. Results appear above the form for quick review.
5. Use Download CSV for spreadsheets, or Download PDF for reports.

1) What heat calorimetry measures

Heat calorimetry connects temperature change to energy transfer during heating, cooling, or mixing. In a cup calorimeter, heat gained by one part of the system balances heat lost by another, allowing unknown heat or final temperature to be inferred from measurements. You can also solve for mass, specific heat, or required temperature change using the same relationships.

2) Core quantities and units

Sensible heating uses mass m, specific heat c, and ΔT. Phase-change problems use latent heat L. This calculator accepts g/kg and °C/K and reports results in joules for consistent comparison.

3) Sensible heat in common materials

Water is a standard reference with c ≈ 4.186 J/g·°C near room temperature. Metals are lower: aluminum 0.900 J/g·°C, copper 0.385 J/g·°C. With the same heat input, low-c materials show larger temperature rises.

4) Latent heat and phase change

During melting or boiling, temperature can remain nearly constant while energy changes phase. Useful references include ice fusion L ≈ 334 kJ/kg and water vaporization L ≈ 2256 kJ/kg. Enter values in kJ/kg or J/g to match lab tables.

5) Mixing calorimetry and equilibrium

When hot and cold samples mix, the final temperature must lie between the initial values. Larger mass or higher heat capacity pulls the equilibrium closer to its starting temperature. Including a calorimeter heat capacity C_cal accounts for the cup, lid, and probe absorbing heat.

6) Calorimeter constant and loss correction

Real setups leak heat to the room. A simple correction is a loss fraction f (for example 0.02–0.10 for 2–10% loss), which nudges the energy balance toward realistic conditions. If you have a measured C_cal, enter it for better accuracy. In short trials, losses are smaller; in long trials, they can dominate.

7) Typical data you may enter

When a datasheet is missing, typical specific heats are: ethanol 2.44 J/g·°C, ice (near 0 °C) 2.09 J/g·°C, and many stainless steels around 0.50 J/g·°C. Use values that match temperature range and material grade when possible.

8) Measurement tips and uncertainty

Stir gently, record temperatures quickly, and keep units consistent. Uncertainty in ΔT matters most when the change is small, while mass uncertainty scales linearly into heat. Report assumptions about losses and C_cal alongside your result.

1) Why is the final mixing temperature between the two starting temperatures?

Energy flows from hotter to colder until equilibrium. In an approximately isolated calorimeter, the final temperature cannot exceed the hottest start or drop below the coldest start.

2) What should I enter for the calorimeter heat capacity (Ccal)?

Use a calibrated value if you have one. If not, 10–100 J/°C is a common starting range for foam-cup setups, but calibrating with known water masses gives the best estimate.

3) When do I use latent heat instead of m·c·ΔT?

Use latent heat when a phase change occurs, like melting ice or boiling water. Significant energy is absorbed or released while temperature stays nearly constant during the transition.

4) Why does the calculator ask for heat-loss fraction?

Real calorimeters lose heat to the environment. A loss fraction provides a simple correction when insulation is imperfect or measurements take longer, reducing bias in calculated heat or equilibrium temperature.

5) Which specific heat value should I choose?

Prefer a datasheet or lab manual value at your temperature range. Composition and temperature can change specific heat, so cite your source and avoid mixing values from different conditions.

6) How can I sanity-check the result quickly?

Use a rough estimate: 100 g of water warmed by 10 °C needs about 4.2 kJ. If your answer is far off, recheck units (g vs kg) and whether a phase change was included.

7) Why might my experimental result differ from theory?

Common causes are heat loss, incomplete mixing, delayed temperature reading, evaporation, or incorrect material properties. Including Ccal, using consistent units, and minimizing timing delays usually improves agreement.