Table of Contents
Specific Heat Capacity and Calorimetry
1. Introduction
Specific heat capacity and calorimetry explain how substances absorb, store and release thermal energy.
Different materials require different amounts of heat to produce the same temperature change. For example, water requires considerably more heat than an equal mass of copper to increase its temperature by the same amount.
These concepts are important in thermodynamics, engineering, climate science, cooking, industrial processes and energy management.
2. Heat Capacity
2.1 Definition
Heat capacity is the amount of heat required to raise the temperature of an entire body by one kelvin or one degree Celsius.
[
C=\frac{Q}{\Delta T}
]
Where:
- (C) = heat capacity
- (Q) = heat supplied
- (\Delta T) = temperature change
The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity depends on the mass and material of the body.
2.2 Factors Affecting Heat Capacity
Heat capacity depends on:
- Mass of the body
- Type of material
- Physical state
- Temperature range
- Conditions under which heat is supplied
A large body of a material generally has a greater heat capacity than a smaller body of the same material.
3. Specific Heat Capacity
3.1 Definition
Specific heat capacity is the amount of heat required to raise the temperature of one kilogram of a substance by one kelvin, without a change of state.
It is represented by (c).
The SI unit is joule per kilogram per kelvin (J kg⁻¹ K⁻¹).
For a substance with approximately constant specific heat capacity:
[
Q=mc\Delta T
]
Where:
- (Q) = heat transferred
- (m) = mass
- (c) = specific heat capacity
- (\Delta T) = temperature change
3.2 Difference Between Heat Capacity and Specific Heat Capacity
| Heat capacity | Specific heat capacity |
|---|---|
| Heat required to raise the temperature of an entire body by one kelvin | Heat required to raise the temperature of one kilogram of a substance by one kelvin |
| Depends on the mass and material of the body | Characteristic of the material under specified conditions |
| Unit: J/K | Unit: J/(kg·K) |
| Represented by (C) | Represented by (c) |
The relationship is:
[
C=mc
]
3.3 Specific Heat Capacity of Common Substances
Approximate values near ordinary temperatures:
| Substance | Specific heat capacity (J kg⁻¹ K⁻¹) |
|---|---|
| Water | 4186 |
| Ice | 2100 |
| Steam | 2000 |
| Aluminium | 900 |
| Iron | 450 |
| Copper | 385 |
| Lead | 128 |
| Sand | 800 |
These values are approximate and can vary with temperature, composition and physical conditions.
3.4 Importance of High Specific Heat Capacity of Water
Water has a relatively high specific heat capacity.
Consequently, it can absorb or release substantial amounts of heat without undergoing a very large temperature change.
This property has important applications:
- Oceans and lakes moderate regional climates.
- Water is used in vehicle cooling systems.
- Water is used in industrial cooling processes.
- Hot-water systems store thermal energy.
- Water-based heating systems distribute heat.
- Coastal regions often experience smaller temperature variations than inland regions.
4. Factors Influencing Specific Heat Capacity
Specific heat capacity is influenced by:
- Chemical composition
- Molecular structure
- Physical state
- Temperature
- Pressure, particularly for gases
Specific heat capacity is not always perfectly constant over a wide temperature range. In accurate calculations, temperature-dependent values may be required.
5. Specific Heat Capacity of Gases
Gases can be heated under different physical conditions.
Two important specific heat capacities are:
5.1 Specific Heat at Constant Volume
Specific heat at constant volume is the heat required to raise the temperature of one kilogram of a gas by one kelvin while its volume remains constant.
It is represented by (c_v).
5.2 Specific Heat at Constant Pressure
Specific heat at constant pressure is the heat required to raise the temperature of one kilogram of a gas by one kelvin while its pressure remains constant.
It is represented by (c_p).
For an ideal gas:
[
c_p>c_v
]
This is because, at constant pressure, some supplied heat is used to perform expansion work in addition to increasing internal energy.
For an ideal gas on a molar basis:
[
C_p-C_v=R
]
Where:
- (C_p) = molar heat capacity at constant pressure
- (C_v) = molar heat capacity at constant volume
- (R) = universal gas constant
6. Calorimetry
6.1 Definition
Calorimetry is the experimental measurement of heat transferred during physical or chemical processes.
An instrument used to measure heat exchange is called a calorimeter.
Calorimetry is used to determine:
- Specific heat capacity
- Heat capacity
- Latent heat
- Heat of reaction
- Energy content of fuels and food
- Thermal properties of materials
6.2 Principle of Calorimetry
The principle of calorimetry is based on the law of conservation of energy.
In an ideal insulated system:
Heat lost by hotter bodies equals heat gained by colder bodies.
[
Q_{lost}=Q_{gained}
]
For a system involving several bodies:
[
\sum Q=0
]
The sign convention must be used consistently. Heat gained is generally taken as positive and heat lost as negative.
In practical experiments, heat exchange with the surroundings and the heat capacity of the calorimeter may also need to be considered.
7. Types of Calorimeters
7.1 Mixing Calorimeter
A mixing calorimeter is used to determine heat exchange when substances at different temperatures are mixed.
It commonly consists of an insulated container, a thermometer and a stirrer.
7.2 Bomb Calorimeter
A bomb calorimeter measures the heat released during combustion of a substance.
The sample burns in a strong sealed vessel containing oxygen, and the temperature rise of the surrounding water and calorimeter is measured.
It is widely used to determine the energy content of fuels and food.
7.3 Differential Scanning Calorimeter
A differential scanning calorimeter (DSC) measures differences in heat flow between a sample and a reference as temperature changes.
It is used in material science, pharmaceuticals, polymers and chemical research.
8. Calorimetry and Change of State
When a substance changes state, heat may be transferred without a corresponding change in temperature during the phase transition at constant pressure.
This heat is called latent heat.
The relationship between heat and specific latent heat is:
[
Q=mL
]
Where:
- (Q) = heat transferred
- (m) = mass
- (L) = specific latent heat
Latent heat is discussed in detail in Section 3.5.
9. Applications of Specific Heat Capacity and Calorimetry
- Water is used as a coolant in engines.
- Oceans moderate coastal temperatures.
- Calorimeters measure the energy released by fuels.
- Food energy is measured using calorimetric methods.
- Industrial plants use thermal energy calculations to control processes.
- Building materials are evaluated for thermal performance.
- Heating systems are designed using heat capacity calculations.
- Material testing determines specific heat capacity for engineering applications.
10. Worked Examples
Example 1: Heat Required to Raise Temperature
Calculate the heat required to raise the temperature of 2 kg of water from 20°C to 50°C. Take the specific heat capacity of water as 4186 J kg⁻¹ K⁻¹.
[
Q=mc\Delta T
]
[
\Delta T=50-20=30,K
]
[
Q=2\times4186\times30
]
[
Q=251,160,J
]
Answer: 251.16 kJ.
Example 2: Calculating Specific Heat Capacity
A 0.5 kg metal block absorbs 5000 J of heat and its temperature increases by 20 K. Calculate its specific heat capacity.
[
c=\frac{Q}{m\Delta T}
]
[
c=\frac{5000}{0.5\times20}
]
[
c=500,J,kg^{-1}K^{-1}
]
Answer: 500 J kg⁻¹ K⁻¹.
Example 3: Heat Capacity
A body absorbs 2400 J of heat and its temperature rises by 10 K. Calculate its heat capacity.
[
C=\frac{Q}{\Delta T}
]
[
C=\frac{2400}{10}
]
[
C=240,J/K
]
Answer: 240 J/K.
Example 4: Principle of Calorimetry
A 0.2 kg metal block at 100°C is placed in 0.3 kg of water at 20°C. The final temperature is 25°C. Assuming no heat loss and taking the specific heat capacity of water as 4200 J kg⁻¹ K⁻¹, calculate the specific heat capacity of the metal.
Heat lost by metal equals heat gained by water.
[
m_mc_m(T_m-T_f)=m_wc_w(T_f-T_w)
]
Substituting:
[
0.2c_m(100-25)=0.3\times4200\times(25-20)
]
[
15c_m=6300
]
[
c_m=420,J,kg^{-1}K^{-1}
]
Answer: 420 J kg⁻¹ K⁻¹.
Example 5: Comparing Heat Requirements
Calculate the heat needed to raise the temperature of 1 kg of copper by 10 K. Take its specific heat capacity as 385 J kg⁻¹ K⁻¹.
[
Q=mc\Delta T
]
[
Q=1\times385\times10
]
[
Q=3850,J
]
Answer: 3850 J.
11. Important Examination Distinctions
| Concept | Meaning | SI unit |
|---|---|---|
| Heat capacity | Heat required to raise the temperature of a body by one kelvin | J/K |
| Specific heat capacity | Heat required to raise 1 kg of a substance by one kelvin | J/(kg·K) |
| Calorimetry | Measurement of heat exchange | No single unit |
| Calorimeter | Instrument used to measure heat exchange | Not applicable |
| (c_p) | Specific heat capacity at constant pressure | J/(kg·K) |
| (c_v) | Specific heat capacity at constant volume | J/(kg·K) |
| Latent heat | Heat transferred during a change of state | J |
| Specific latent heat | Heat required per unit mass for a phase change | J/kg |
12. 36 Key Takeaways for Exams
- Heat capacity is the heat required to raise the temperature of a body by one kelvin.
- The SI unit of heat capacity is J/K.
- Specific heat capacity is the heat required to raise the temperature of one kilogram of a substance by one kelvin.
- The SI unit of specific heat capacity is J/(kg·K).
- Specific heat capacity is represented by (c).
- Heat capacity is represented by (C).
- Heat capacity is related to specific heat capacity by (C=mc).
- Heat required for a temperature change is calculated using (Q=mc\Delta T).
- The specific heat capacity of water is approximately 4186 J kg⁻¹ K⁻¹ near ordinary temperatures.
- Water has a relatively high specific heat capacity.
- High specific heat capacity allows water to absorb considerable heat with a comparatively small temperature rise.
- Oceans help moderate the climate because of water’s high specific heat capacity.
- Water is commonly used as a coolant in engines and industrial systems.
- Specific heat capacity varies among different materials.
- Specific heat capacity may change with temperature and physical conditions.
- Calorimetry is the measurement of heat transferred during physical or chemical processes.
- A calorimeter is an instrument used in calorimetry.
- The principle of calorimetry is based on conservation of energy.
- In an ideal insulated system, heat lost equals heat gained.
- Heat exchange with surroundings may affect practical calorimetry results.
- A mixing calorimeter measures heat exchange when substances are mixed.
- A bomb calorimeter measures heat released during combustion.
- Differential scanning calorimetry measures heat-flow differences during controlled temperature changes.
- Gases have different specific heat capacities at constant pressure and constant volume.
- Specific heat capacity at constant pressure is represented by (c_p).
- Specific heat capacity at constant volume is represented by (c_v).
- For an ideal gas, (c_p) is greater than (c_v).
- For an ideal gas on a molar basis, (C_p-C_v=R).
- At constant pressure, a gas may perform expansion work when heated.
- The heat required for a temperature change depends on mass, specific heat capacity and temperature change.
- A temperature interval of 1 K equals an interval of 1°C.
- Latent heat is transferred during a change of state without a temperature change during the phase transition at constant pressure.
- Specific latent heat is heat transferred per unit mass during a phase change.
- Specific heat capacity is an important property in material selection and thermal engineering.
- Calorimetry is used in determining the energy content of fuels and food.
- Specific heat capacity and calorimetry are fundamental to thermodynamics and energy management.