Calorimeter - Definition, Uses, Types, Application, Diagram, FAQs

Definition of Calorimetry

Calorimetry is the process used to measure heat transfer during temperature change or phase change. A device called a calorimeter is used to calculate this heat exchange.

Principle of Calorimeter

The working of a calorimeter is based on the Law of Conservation of Energy.
Heat lost by the hotter body = Heat gained by the colder body
When a hot object is placed in contact with a cold object, heat flows from the hotter to the colder one until both reach the same temperature.

Calorimetry Formula

$$
Q=m c \Delta T
$$

Where:

• $\mathbf{Q}=$ Heat gained/lost
• $\mathbf{m}=$ Mass
• $\mathbf{c}=$ Specific heat capacity
• $\boldsymbol{\Delta} \mathbf{T}=$ Change in temperature

In calorimetry problems:
Heat lost $=$ Heat gained

Calorimeter - Explanation in Detail

The physical instrument or device which is used in the measurements of heat-related stuff (that is mainly used in the study of calorimetry). The construction of the calorimeter contains vessels made up of good conductors like metals. The composition of metallic vessels contains copper and aluminium in major. The contents of the metallic vessel are facilitated for stirring with the help of a stirrer. The heat loss in the stirrer is reduced with the help of an insulated jacket around the stirrer. The thermometer is allowed to be inserted through a small opening which is used to measure the thermal change that occurs inside the calorimeter.

In the inner part of the calorimeter, some sample of fuel is used to burn. The metallic vessel contains water, when the fuel inside is burnt, the water gets heated. The heat loss of the fuel is converted into the heat gained by the water. That is, energy is conserved. To increase the accuracy of results, heat loss can be terminated by the insulation of the calorimeter instrument from the environmental conditions. The heat change of the water is measured by using the inserted thermometer. The readings are used to find the heat capacity of the water and the amount of energy conserved inside the fuel.

Uses of Calorimetry

Calorimetry is widely used in:

• Food industry to find calories in food
• Medical science to measure body metabolism
• Physics and chemistry labs to study reactions
• Engineering for designing cooling and heating systems
• Energy sector to test fuels
• Material science to study thermal properties

Types of Calorimeters

Different processes need different calorimeters.
Common types include:
1. Adiabatic Calorimeter - Prevents heat exchange with surroundings
2. Constant Pressure Calorimeter - Used in chemistry labs
3. Reaction Calorimeter - Measures heat during chemical reactions
4. Differential Scanning Calorimeter (DSC) - Used in material testing
5. Bomb Calorimeter - Used to find the calorific value of fuels

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Solved Examples Based on the Calorimetry Principle

Example 1
The principle of calorimetry is based on:
1. Conservation of mass
2. Conservation of energy
3. Conservation of momentum
4. Both (1) and (2)

Solution: Heat lost $=$ Heat gained → law of conservation of energy.
Answer: (2)

Example 2 :An unknown metal (mass $\mathbf{1 9 2 ~ g}$ ) at $\mathbf{1 0 0}^{\boldsymbol{\circ}} \mathbf{C}$ is placed into a brass calorimeter (mass $\mathbf{1 2 8 ~ g}$ ) containing $\mathbf{2 4 0 ~ g}$ water at $\mathbf{8 . 4}^{\boldsymbol{\circ}} \mathbf{C}$. The final temperature is $\mathbf{2 1 . 5}^{\boldsymbol{\circ}} \mathbf{C}$. Find the specific heat s of the metal.
Options:
1. $458 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$
2. $1232 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$
3. $654 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$
4. $916 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$
(Specific heat: brass $=394 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ )
Solution :
Convert masses to kg: m_m = 0.192 kg , m_brass = 0.128 kg , m_water = 0.240 kg .
Heat lost by metal = Heat gained by brass + water:

$
0.192 s(100-21.5)=0.128 \times 394(21.5-8.4)+0.240 \times 4200(21.5-8.4)
$

Solving gives $s \approx 916 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$.
Answer: (4)

Example 3
A liquid of mass $m$ and specific heat $C$ is at temperature $2 T$. Another liquid of mass $m / 2$ and specific heat $\mathbf{2 C}$ is at temperature T. They are mixed. The final temperature is:
Options:
1. $\frac{2 T}{3}$
2. $\frac{8 T}{5}$
3. $\frac{3 T}{5}$
4. $\frac{3 T}{2}$

Solution: Use $\theta_{\text {mix }}=\frac{m_1 c_1 \theta_1+m_2 c_2 \theta_2}{m_1 c_1+m_2 c_2}$.

$
\theta=\frac{m C \cdot 2 T+\frac{m}{2} \cdot 2 C \cdot T}{m C+\frac{m}{2} \cdot 2 C}=\frac{2 m C T+m C T}{2 m C}=\frac{3 T}{2} .
$

Answer: (4)

Example 4
Ice at $\mathbf{- 2 0} \mathbf{~ C}^{\boldsymbol{\circ}} \mathbf{C}$ is added to $\mathbf{5 0 ~ g}$ water at $\mathbf{4 0}^{\boldsymbol{\circ}} \mathbf{C}$. After reaching $\mathbf{0}^{\boldsymbol{\circ}} \mathbf{C}$, $\mathbf{2 0 ~ g}$ ice remains unmelted. The amount of ice added was:

Options:
1. 100 g
2. 50 g
3. 40 g
4. 60 g
(Specific heats: water $4.2 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}$, ice $2.1 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}$; latent heat of fusion $=334 \mathrm{~J} / \mathrm{g}$ )
Solution: Let total ice $=\mathrm{mg}$. Heat taken by ice to reach $0^{\circ} \mathrm{C}$ and melt (only $\mathrm{m}-20$ melts) equals heat lost by water cooling $40 \rightarrow 0^{\circ} \mathrm{C}$.

Equation:

$
20 \times 2.1 \times m+(m-20) \times 334=50 \times 4.2 \times 40
$

Solving yields $m \approx 40 \mathrm{~g}$.
Answer: (3)

Example 5 : 5 g water at $10^{\circ} \mathrm{C}$ is mixed with 5 g water at $40^{\circ} \mathrm{C}$. Final temperature is:
Options:
1. $20^{\circ} \mathrm{C}$
2. $25^{\circ} \mathrm{C}$
3. $30^{\circ} \mathrm{C}$
4. $35^{\circ} \mathrm{C}$

Solution: Equal masses and same specific heat → average temperature:

$
\theta=\frac{10+40}{2}=25^{\circ} \mathrm{C} .
$

Answer: (2)

Summary

Calorimetry is the study of heat transfer during physical changes or chemical reactions, governed by the principle of conservation of energy. A calorimeter measures heat exchange between substances, such as the heat lost by a hotter object being equal to the heat gained by a cooler one. This principle has applications in various fields, from everyday activities like boiling water to complex scientific and industrial processes.