Calorimetry

A thermometer tells you how hot something is, but it doesn't tell you how much heat energy an object contains or exchanges. To answer that question, scientists developed a technique called calorimetry and a device called a calorimeter.

Calorimetry is the science of measuring heat exchange during physical or chemical processes. The word comes from the Latin calor (heat) + Greek metron (measure).

A calorimeter is a cylindrical vessel which is used to measure the amount of heat gained (or lost) by a body when it is mixed with another body or substance.

A calorimeter is an insulated device used to measure the heat gained or lost by a substance during a thermal process. It works on a simple idea: trap all the heat inside the device so nothing escapes, and then measure the temperature change.

Fig.: Cross-section of a simple water calorimeter showing all key components

Fig.: A calorimeter works just like a thermos flask — both trap heat inside using insulation

The entire working of a calorimeter is based on one fundamental law of physics — the Law of Conservation of Energy. Since the calorimeter is thermally insulated, no heat enters or leaves the system. This means:

Principle of Calorimetry: In an isolated system, the total heat lost by the hot body is exactly equal to the total heat gained by the cold body.
Heat Lost = Heat Gained

Fig.: Heat flows from the hot object to the cold water and calorimeter until thermal equilibrium is reached

The method of mixtures is the standard experimental technique for determining the specific heat capacity of an unknown substance using a calorimeter.

Procedure:

Let's build the master formula step by step. First, define all our variables clearly.

Variable Definitions

Step-by-Step Derivation

Problem: A 0.06 kg aluminium sphere is heated to 100°C and placed in a 0.12 kg copper calorimeter containing 0.30 kg of water at 25°C. The mixture reaches a steady temperature of 28°C. Find the specific heat capacity of aluminium.

Solution:

Given:
Mass of aluminium sphere (m₁) = 0.06 kg
Mass of copper calorimeter (m₂) = 0.12 kg
Mass of water (m₃) = 0.30 kg
Specific heat of copper (s₂) = 387 J kg⁻¹ K⁻¹
Specific heat of water (s₃) = 4180 J kg⁻¹ K⁻¹
Initial temp of sphere (T₁) = 100°C
Initial temp of water + calorimeter (T₂) = 25°C
Final equilibrium temp (T) = 28°C

Step 1: Calculate temperature changes

• Temperature drop of sphere: T₁ − T = 100 − 28 = 72°C
• Temperature rise of water & calorimeter: T − T₂ = 28 − 25 = 3°C

Step 2: Apply Eq.

Step 3: Substitute values

Step 4: Compute the numerator

• 0.12 × 387 = 46.44
• 0.30 × 4180 = 1254
• Sum = 46.44 + 1254 = 1300.44
• Numerator = 1300.44 × 3 = 3901.32

Step 5: Compute the denominator

• 0.06 × 72 = 4.32

Step 6: Final answer

• Calorimeter: An insulated device used to measure heat transfer during a process.
• Principle of Calorimetry: Heat lost = Heat gained (energy is conserved).
• Method of Mixtures: Heat a sample, place it in the calorimeter, and measure the temperature change to calculate the heat.
• Formula: Used to calculate the specific heat of a substance from measured temperatures and masses.
• Good Practice: Transfer the sample quickly and stir well for accurate results.
• Why Water is Used: Water has high specific heat, so it absorbs a lot of heat without a large temperature change.