About

Calorimetry quantifies heat exchange during thermal processes. The foundational equation Q = m × c × ΔT links energy transfer to mass, material composition, and temperature change. Errors in specific heat selection or unit conversion propagate linearly into the result. A misidentified alloy or a Fahrenheit/Celsius confusion produces answers off by orders of magnitude. This tool uses tabulated c values sourced from NIST and engineering handbooks for 30+ substances, handles automatic unit conversion across Joules, calories, BTU, and Watt-hours, and solves multi-substance thermal equilibrium problems where T_f is unknown.

The mixing mode solves for equilibrium temperature by enforcing conservation of energy: the net heat exchanged across all bodies equals zero. This assumes no phase transitions occur within the temperature range, no heat loss to the environment, and perfect thermal contact. For systems near a substance's melting or boiling point, latent heat contributions are not modeled here and require a more specialized phase-change analysis. Pro tip: real calorimeters have a "calorimeter constant" representing their own heat capacity. Account for it by adding the calorimeter as an additional substance in the mixing calculation.

Formulas

The fundamental calorimetry equation relates heat energy transferred to a body's mass, its material-specific heat capacity, and the temperature difference experienced:

Q = m × c × ΔT

Where Q = heat energy J, m = mass kg, c = specific heat capacity J/(kg⋅K), ΔT = T_final − T_initial in °C or K. A positive Q indicates heat absorbed (endothermic). A negative Q indicates heat released (exothermic).

For thermal equilibrium between n substances in contact with no heat loss to surroundings, conservation of energy requires:

n∑i=1 m_i × c_i × (T_f − T_i) = 0

Solving for the unknown equilibrium temperature T_f:

T_f = n∑i=1 m_i ⋅ c_i ⋅ T_in∑i=1 m_i ⋅ c_i

Temperature conversions used internally:

T_°C = (T_°F − 32) × 59

T_K = T_°C + 273.15

Energy unit conversions: 1 cal = 4.184 J, 1 BTU = 1055.06 J, 1 Wh = 3600 J.

Reference Data

Substance	Specific Heat c J/(kg⋅K)	Density kg/m³	Melting Point °C	Boiling Point °C
Water (liquid)	4186	997	0	100
Ice	2090	917	-	0
Steam	2010	0.6	100	-
Aluminum	897	2700	660	2519
Copper	385	8960	1085	2562
Iron	449	7874	1538	2862
Steel (carbon)	502	7850	1425	2750
Lead	129	11340	327	1749
Gold	129	19300	1064	2856
Silver	235	10490	962	2162
Titanium	523	4507	1668	3287
Zinc	388	7134	420	907
Tin	228	7265	232	2602
Nickel	444	8908	1455	2913
Brass	380	8500	930	-
Glass (soda-lime)	840	2500	573	-
Granite	790	2750	1260	-
Marble	880	2711	-	-
Concrete	880	2400	-	-
Wood (oak)	2380	750	-	-
Ethanol	2440	789	−114	78
Methanol	2510	792	−98	65
Glycerin	2430	1261	18	290
Olive Oil	1970	911	−6	300
Mercury	139	13546	−39	357
Air (dry, 20°C)	1005	1.2	-	-
Sand (quartz)	830	1520	1710	2230
Soil (average)	800	1500	-	-
Rubber	2010	1100	-	-
Polyethylene (HDPE)	1900	960	130	-

Frequently Asked Questions

A negative Q means the substance released heat (exothermic process). This occurs when T_final < T_initial. The sign convention follows thermodynamic standard: positive Q = heat absorbed, negative Q = heat released.

No. The equation Q = mcΔT applies only within a single phase. If your temperature range crosses a melting or boiling point (e.g., heating water from −10°C to 110°C), you must separately calculate the sensible heat for each phase and add latent heat (Q = mL) at each transition. A warning is displayed if water crosses 0°C or 100°C.

Values are tabulated at approximately 25°C and 1atm pressure, sourced from NIST and standard engineering references. Specific heat varies with temperature. For example, water's c ranges from 4218 J/(kg⋅K) at 0°C to 4178 at 35°C. For most engineering estimates below 500°C, the tabulated values introduce less than 2% error.

Yes. The mixing calculator supports up to 10 substances simultaneously. Each substance can have a different mass, initial temperature, and specific heat. The equilibrium temperature T_f is computed from the weighted average formula. Add substances using the "Add Substance" button.

The equilibrium temperature is a thermal-capacity-weighted average. A substance with higher m × c product dominates. For example, 1kg of water (c = 4186) mixed with 1kg of copper (c = 385) yields T_f heavily skewed toward the water's initial temperature because water's thermal capacity is 10.9× larger.

Use the energy unit selector below the result. The calculator converts automatically: 1 cal = 4.184 J, 1 kcal = 4184 J, 1 BTU = 1055.06 J, 1 Wh = 3600 J. All conversions are exact to the precision shown.