Calorimetry Heat Transfer Calculator

Calorimetry measures heat flow in chemical and physical processes.

The fundamental formula:

q = m × c × ΔT

Where:

• q = heat transferred (joules, J)
• m = mass (grams)
• c = specific heat capacity (J/g·°C)
• ΔT = T_final − T_initial (degrees Celsius or Kelvin, since a difference of one is the same in both)

Coffee-cup calorimetry: For a reaction occurring in aqueous solution:

q_reaction = −q_solution = −m_solution × c_solution × ΔT

Assuming c_solution ≈ 4.184 J/g·°C, since a dilute aqueous solution is close enough to water.

Specific heat capacities (c) at 25°C:

Worked example

A coffee-cup calorimeter holds 100.0 g of solution. You add 0.100 mol of a solute and the thermometer goes from 25.0 °C to 31.5 °C.

q = 100.0 × 4.184 × 6.5 = 2,719.60 J, or 2.7196 kJ

The water gained that heat, so the reaction gave it up. Flip the sign for the reaction and divide by the moles:

ΔH = −2.7196 ÷ 0.100 = −27.196 kJ/mol, exothermic

Two things to notice. The mass is the whole solution, not the solute, because it is the whole solution the thermometer is sitting in. And a 6.5-degree rise on a hundred grams is only about two and a half kilojoules, which is why coffee-cup calorimetry works at all: the quantities are small enough that a polystyrene cup loses very little of it during the half-minute the measurement takes.

Sign convention:

• q > 0: system absorbs heat (endothermic)
• q < 0: system releases heat (exothermic)

Converting units:

• 1 calorie (cal) = 4.184 J
• 1 food Calorie (kcal) = 4184 J
• 1 BTU = 1055.06 J

Molar enthalpy: If the number of moles is known, the molar enthalpy change:

ΔH = q_reaction / n = −q_solution / n (kJ/mol)

Watch that minus sign. The thermometer measures what happens to the water, not to the reaction, and the two have opposite signs. A neutralization that warms the water by 6 degrees has a positive q for the solution and a negative ΔH for the reaction. Report the reaction’s sign, because that is what a textbook or a data table means by ΔH.

What “coffee cup” actually means

The name is literal. A coffee-cup calorimeter is a polystyrene cup, or two nested for insulation, with a lid, a thermometer and a stirrer. It works because polystyrene conducts heat poorly and the reaction is over in seconds, so very little heat escapes during the measurement. It also works at constant pressure, open to the room, which is precisely the condition under which the heat you measure equals the enthalpy change. That is not a coincidence of definitions but the reason ΔH is defined at constant pressure in the first place.

A bomb calorimeter is the sealed rigid alternative, used for combustion. It runs at constant volume, so what it measures is ΔU rather than ΔH, and the two differ by the work the gases would have done pushing the atmosphere back.

A note on units

The specific heat here is per degree Celsius, but you can use the same number per kelvin without converting anything, because a temperature difference of one degree Celsius is a difference of exactly one kelvin. Only absolute temperatures need converting. This trips people up constantly, and it works in your favour: ΔT never needs a conversion in this equation.