Calorimetry Calculator — Heat Exchange & Coffee-Cup Enthalpy

What is calorimetry?

The calorimetry calculator can help you solve complex calorimetry problems. It can analyze the heat exchange between up to 3 objects. Additionally, it can find the enthalpy change of a chemical reaction inside a coffee-cup calorimeter. Read on to learn what calorimetry is and how to solve calorimetry problems with the proper equations.

Calorimetry is a science where you try to find the heat transfer during a chemical reaction, phase transition, or temperature change. Calorimetry experiments are based on the law of conservation of energy. This law states that the total energy of an isolated system is constant.

In physics, heat is also known as thermal energy. So, if there is an isolated system where objects exchange heat, the total heat change equals 0:

0 = ΔQ₁ + ΔQ₂ + ... + ΔQᵢ

Objects tend towards thermal equilibrium. So, two objects of different temperatures will exchange heat on contact. The object with a higher temperature will give away heat, while the other will absorb it. After some time, they will have the same temperature.

Calorimetry equation

It's not easy to measure the heat transfer directly. That's why we use constant-pressure calorimeters — containers that provide constant pressure and thermal isolation from the surroundings. In a calorimeter, we can measure temperature change with a thermometer. This equation binds temperature change and heat:

Q = m · c · ΔT

where:

• Q — heat (thermal energy), in joules (J) or BTU;
• m — mass of the object, in kilograms (kg) or pounds (lb);
• c — specific heat capacity of the material, in J/(kg·K) or BTU/(lb·°F); and
• ΔT — change in temperature, ΔT = T_final − T_initial.

When several objects exchange heat and reach a common final temperature (the equilibrium temperature T_eq), conservation of energy gives:

T_eq = Σ(mᵢ · cᵢ · Tᵢ) / Σ(mᵢ · cᵢ)

How to solve calorimetry problems?

1. Identify every object that exchanges heat, and note its mass, specific heat, and starting temperature.
2. Write the energy-balance equation: the heat lost by the hot objects equals the heat gained by the cold ones (the total is zero).
3. Solve for the unknown — usually the equilibrium temperature T_eq.
4. Back-substitute T_eq to find the heat Q exchanged by each object.

Calorimetry problems – example 1

Suppose you drop a 0.3 kg piece of aluminum (c = 897 J/(kg·K)) heated to 90 °C into 0.5 kg of water (c = 4186 J/(kg·K)) at 20 °C. Enter both objects in the heat exchange mode and the calculator returns the equilibrium temperature (about 28 °C) and the heat each object gains or loses.

Calorimetry problems — example 2

Add a third object — for example a 0.2 kg copper block (c = 385 J/(kg·K)) at 50 °C. Switch the number of objects to 3 and the calculator balances the heat across all three bodies at once, again reporting the single equilibrium temperature they all settle at.

Chemical reaction in a coffee-cup calorimeter

A coffee-cup calorimeter is a simple constant-pressure device used to measure the enthalpy change ΔH of a reaction that happens in solution. The heat released or absorbed by the reaction is taken up by the solution, so:

Q = m · c · ΔT
ΔH = − Q / n

where m is the mass of the solution, c its specific heat, ΔT the measured temperature change, and n the number of moles of the limiting reactant. A negative ΔH means the reaction is exothermic (releases heat); a positive ΔH means it is endothermic (absorbs heat).

How to use the calorimetry calculator?

1. Pick your unit system — Metric (SI) or American (US customary).
2. Choose a mode: heat exchange between objects, or coffee-cup calorimeter (enthalpy).
3. In heat-exchange mode, select 2 or 3 objects and enter each object's mass, specific heat (use the material presets for common substances) and initial temperature.
4. In coffee-cup mode, enter the solution mass and specific heat, the initial and final temperatures, and the moles of the limiting reactant.
5. Click Calculate to see the equilibrium temperature or the molar enthalpy change.

FAQs

What units does the calorimetry calculator support?

Both the metric (SI) system — kg, °C, J/(kg·K), J, kJ/mol — and the American (US customary) system — lb, °F, BTU/(lb·°F), BTU, BTU/mol.

Does using °C or °F instead of kelvin change the result?

For the equilibrium temperature and for Q = m·c·ΔT it does not, because only temperature differences matter, and a 1 °C change equals a 1 K change (and a 1 °F change equals a 1 °R change).

Why is my reaction's ΔH negative?

A negative ΔH means the reaction released heat into the solution (the solution warmed up): the reaction is exothermic. A positive ΔH means the solution cooled down because the reaction absorbed heat — it is endothermic.