General Chemistry I · Energy and Thermodynamics

Calorimetry

8 min read

On this page 7 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Study tools

In 30 seconds

measures the heat exchanged during a change by trapping it and observing the resulting temperature change. Heat capacity C is the heat needed to raise an object's temperature by 1 °C; specific heat capacity c is the heat needed to raise 1 g by 1 °C. A runs at constant pressure for solution reactions; a runs at constant volume for combustion. In both, heat gained by the surroundings equals heat lost by the reaction, so q_reaction = -q_calorimeter.

Why this matters

Bomb calorimetry measures the Calorie content printed on food labels: a weighed portion is burned in oxygen, the temperature rise is recorded, and the heat released is converted to food Calories (1 Cal = 4184 J). Clinical and sports-nutrition estimates of energy expenditure trace back to these measurements. Hospital labs use calorimetric data to choose reactions that must not run too hot or cold, and instant hot/cold packs are designed around the specific heats of their contents.

The college version

1. Heat Capacity and Specific Heat Capacity

Heat capacity C is the heat required to raise an object's temperature by 1 °C (units J/°C). It depends on how much and what kind of substance is present — a swimming pool has a far larger C than a cup of water. Specific heat capacity c is the heat required to raise exactly 1 g of a substance by 1 °C (units J/(g·°C)); it is an intensive property of the material. The two are related by C = mc, where m is mass. Water's unusually high specific heat (4.184 J/(g · ^°C)) is why oceans moderate coastal climates and the body holds a near-constant temperature.

2. Constant-Pressure Calorimetry (Coffee-Cup)

A coffee-cup calorimeter is two nested polystyrene cups with a lid and thermometer. Open to the atmosphere, it holds pressure constant, so the measured heat equals the enthalpy change ΔH (see Topic 12). Reactions run in dilute aqueous solution, so the solution is treated as having water's heat capacity. The solution's heat is q_solution = mcΔT, and by conservation of energy the reaction's heat is equal and opposite:

$q reaction = -q solution = -mc Δ T$

3. Constant-Volume Calorimetry (Bomb)

A bomb calorimeter is a sealed, thick-walled steel vessel submerged in water inside an insulated jacket. A sample is ignited electrically in excess oxygen, and the combustion heat warms the bomb, water, and jacket together. Because volume is fixed, no pressure–volume work occurs, so the measured heat equals the change in internal energy ΔE. The whole apparatus has one calorimeter constant C_cal (J/°C) found by , giving:

$q reaction = -C cal Δ T$

Bomb calorimetry is the standard way to measure a food's energy content.

How it works

Place the reaction in a calorimeter containing a known mass of water (or a calibrated bomb).
Record the initial temperature, run the reaction, and record the final temperature.
Compute ΔT = T_final - T_initial.
For a coffee-cup calorimeter, find q_solution = mcΔT, then q_reaction = -q_solution.
For a bomb calorimeter, find q_cal = C_cal ΔT, then q_reaction = -q_cal.
Interpret the sign: negative means the reaction released heat (exothermic); positive means it absorbed heat (endothermic).

Common confusions

Do not confuse	With	Difference
Heat capacity C	Specific heat capacity c	C is for the whole object (J/°C); c is per gram (J/(g·°C))
Coffee-cup calorimeter	Bomb calorimeter	Constant pressure vs constant volume; ΔH vs ΔE
Calorimeter constant	Specific heat of water	C_cal describes the whole apparatus, not just water
Temperature rise of surroundings	Reaction releasing heat	A rise in surroundings means the reaction lost heat (exothermic)
ΔT in °C	Absolute temperature in K	Only the change is used in q = mcΔT; 1 °C = 1 K for differences

Memory aids

"q = mcΔT, then flip it for the reaction" — calculate the calorimeter's heat with q = mcΔT, then reverse the sign because the reaction's heat is equal and opposite.

Quick review

Topic Recap

Calorimetry turns a temperature change into a heat measurement using q = mcΔT (or q = CΔT). Heat capacity is for a whole object; specific heat capacity is per gram. Coffee-cup calorimeters run at constant pressure and measure ΔH for solution reactions; bomb calorimeters run at constant volume and measure ΔE for combustion via the calorimeter constant. In every case the reaction's heat is the negative of the surroundings' heat, and the sign tells whether the process was exothermic or endothermic.

Knowledge Check

Which has units J/°C? A) specific heat capacity c B) heat capacity C C) temperature D) mass
20.0 g of a substance absorbs 836 J and warms 10.0 °C. Its specific heat (J/(g·°C)) is: A) 0.418 B) 4.18 C) 41.8 D) 836
In a coffee-cup calorimeter a reaction makes the water temperature rise. The reaction is: A) endothermic B) exothermic C) at equilibrium D) impossible to classify
Bomb calorimetry is run at constant: A) pressure B) temperature C) volume D) moles
A bomb calorimeter (C_cal = 10.0 kJ/^°C) rises 1.50 °C when a sample burns. The reaction heat is: A) +15.0 kJ B) −15.0 kJ C) +6.67 kJ D) −6.67 kJ

Answers and Rationales

B — Heat capacity C is J/°C; specific heat c is J/(g·°C).
B — c = q/(mΔT) = 836 J/(20.0 g × 10.0 ^°C) = 4.18 J/(g · ^°C).
B — The water (surroundings) gained heat, so the reaction released heat: exothermic.
C — The sealed steel bomb holds volume constant, so no PΔV work occurs.
B — q_cal = (10.0)(1.50) = +15.0 kJ, so q_reaction = -15.0 kJ.

Eli explains

The same idea, in plain words

Explain it like I’m 10

A calorimeter is a thermos that tells you how much heat a reaction produced. Drop a hot rock into cool water and the rock cools while the water warms — the water "catches" the rock's heat. A calorimeter does this on purpose: it holds a known amount of water (or a sturdy container) around a reaction, measures the temperature rise, and works backward to find the heat. A bathtub barely warms when you add a little heat, but a small cup changes a lot; that "big versus small" heat capacity is exactly what the math captures.

Where this stops being exact: a perfect thermos assumes all the heat goes into the water and none leaks or warms the container. Real calorimeters leak and absorb a little, so chemists measure a correction factor (the calorimeter constant). The perfectly insulated calorimeter exists only on paper.

Simple Example

You place 100.0 g of water at 20.0 °C in a coffee cup, dissolve a salt, and watch the temperature climb to 26.0 °C. That 6.0 °C rise tells you the dissolving released heat to the water; plugging the numbers into q = mcΔT turns the rise into joules.

Worked example

Heat from a temperature change:

$q = mc Δ T or q = C Δ T$

where q is heat (J), m is mass (g), c is specific heat (J/(g·°C)), C is heat capacity (J/°C), and ΔT = T_final - T_initial (°C). Sign: q > 0 means the substance absorbed heat (temperature rose); q < 0 means it released heat. Energy conservation in a calorimeter:

$q reaction = -q calorimeter$

Specific heat of liquid water: c = 4.184 J/(g · ^°C).

Worked Example 1 — Heating water

How much heat raises 250.0 g of water from 22.0 °C to 98.0 °C?

Step 1. Compute ΔT = 98.0 - 22.0 = 76.0 ^°C.

Step 2. Substitute into q = mcΔT:

$q = (250.0 g) (4.184 J g \cdot ° C)(76.0 ° C) = 7.95 \times 104 J = 79.5 kJ$

The positive sign means the water absorbed 79.5 kJ.

Worked Example 2 — Coffee-cup calorimetry

When 2.00 g of an ionic solid dissolves in 50.0 g of water in a coffee-cup calorimeter, the temperature falls from 25.0 °C to 21.5 °C. Find the heat of dissolving.

Step 1. Total solution mass is m = 50.0 + 2.00 = 52.0 g, with c ≈ 4.184 J/(g · ^°C). The temperature change is ΔT = 21.5 - 25.0 = -3.5 ^°C.

Step 2. Heat of the solution:

$q solution = (52.0 g) (4.184 J g \cdot ° C)(-3.5 ° C) = -7.6 \times 102 J$

Step 3. Heat of the reaction is equal and opposite:

$q reaction = -q solution = +7.6 \times 102 J$

The positive sign means dissolving absorbed heat from the surroundings (the solution cooled) — an endothermic process, consistent with the temperature drop.

Worked Example 3 — Bomb calorimetry

A 0.500 g food sample burns in a bomb calorimeter with C_cal = 8.77 kJ/^°C. The temperature rises from 24.00 °C to 26.50 °C. Find the heat released per gram.

Step 1. ΔT = 26.50 - 24.00 = 2.50 ^°C.

Step 2. Heat absorbed by the calorimeter:

$q cal = C cal Δ T = (8.77 kJ ° C)(2.50 ° C) = 21.9 kJ$

Step 3. Heat released by combustion is q_reaction = -21.9 kJ, or per gram:

$-21.9 kJ 0.500 g = -43.9 kJ/g$

The negative sign shows heat was released (exothermic combustion).

Common setup errors: forgetting to add the solute's mass to the solution mass; mixing up C and c; and dropping the sign on q_reaction = -q_calorimeter. (Using Celsius is safe here because only a temperature difference appears, and 1 °C equals 1 K for differences.)

Key takeaways

High yield: q = mcΔT, with ΔT = T_final - T_initial; the sign of ΔT sets the sign of q.
High yield: q_reaction = -q_calorimeter in every calorimetry problem.
Heat capacity C (J/°C) is extensive; specific heat c (J/(g·°C)) is intensive.
Water's specific heat is 4.184 J/(g · ^°C) — memorize it.
Coffee-cup calorimetry runs at constant pressure and measures ΔH.
Bomb calorimetry runs at constant volume, measures ΔE, and uses C_cal.
A temperature rise in the surroundings means the reaction released heat (exothermic).

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study toolsYou’ll learn to · Key vocabulary

You’ll learn to

Distinguish heat capacity C from specific heat capacity c and give the units of each.
Use q = mcΔT and q = CΔT to calculate heat transfer with correct signs.
Explain how constant-pressure (coffee-cup) calorimetry measures reaction heat from a solution temperature change.
Explain how constant-volume (bomb) calorimetry measures combustion heat using the calorimeter constant.

Key vocabulary

Calorimetry: Measuring heat transfer via a temperature change
Heat capacity (C): Heat to raise an object's temperature by 1 °C (J/°C)
Specific heat capacity (c): Heat to raise 1 g by 1 °C (J/(g·°C))
Δ T: T_final - T_initial
Coffee-cup calorimeter: Insulated open cup at constant pressure
Bomb calorimeter: Sealed steel vessel at constant volume
Calorimeter constant (Ccal): Heat capacity of the whole bomb apparatus
Calibration: Burning a known sample to find C_cal

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.