Last Updated: September 2, 2026
Specific heat capacity is a key concept in thermal physics. It describes the amount of thermal energy required to raise the temperature of 1 kg of a substance by 1°C or 1 K. The main specific heat capacity formula is Q = mcΔT, which is used to calculate thermal energy, temperature change, mass, or specific heat capacity.
Quick Summary
Specific heat capacity is the amount of thermal energy required to raise the temperature of 1 kg of a substance by 1°C or 1 K. The main specific heat capacity formula is Q = mcΔT. The specific latent heat formula is Q = mL, which is used when a substance changes state without a temperature change.
Key Takeaways
- The main specific heat capacity formula is Q = mcΔT.
- To find specific heat capacity, use c = Q/(mΔT).
- The SI unit of specific heat capacity is J/kg·K.
- Q represents thermal energy transferred and is measured in joules.
- ΔT is the change in temperature: Tfinal − Tinitial.
- The specific latent heat formula is Q = mL.
- Specific heat capacity describes temperature changes, while specific latent heat describes changes of state at constant temperature.
- Heat capacity is related to specific heat capacity by C = mc.
Who Is This Guide For?
This guide is designed for high school and college physics students studying thermal physics, heat transfer, specific heat capacity, and latent heat. It is useful for students preparing for physics exams, homework, laboratory work, and numerical problems involving Q = mcΔT and Q = mL.
What Is Specific Heat Capacity?
Specific heat capacity is the amount of thermal energy required to raise the temperature of 1 kg of a substance by 1°C or 1 K.
The symbol for specific heat capacity is c. It is a property of a material, so different substances require different amounts of energy to produce the same temperature increase.
For example, water has a relatively high specific heat capacity. This means that a large amount of thermal energy is required to increase the temperature of water compared with many common metals.
Specific heat capacity is important in thermal physics, heat transfer, cooling systems, climate science, and engineering.
Specific Heat Capacity and latent heat phase change of melting ice
Specific Heat Capacity Formula: Q = mcΔT
The main specific heat capacity formula in physics is:
Q = mcΔT
This equation calculates the thermal energy transferred when the temperature of a substance changes.
Where:
- Q = thermal energy transferred, measured in joules (J)
- m = mass of the substance, measured in kilograms (kg)
- c = specific heat capacity, measured in J/kg·K or J/kg·°C
- ΔT = change in temperature
The temperature change is calculated using:
ΔT = Tfinal − Tinitial
For temperature differences, a change of 1 K is equal in size to a change of 1°C.
Formula for Specific Heat Capacity
If you need to find specific heat capacity, rearrange the main equation:
c = Q/(mΔT)
This is the formula to calculate specific heat capacity when thermal energy, mass, and temperature change are known.
The other useful rearrangements are:
Q = mcΔT
ΔT = Q/(mc)
m = Q/(cΔT)
These equations allow you to solve different types of specific heat capacity problems.
What Is Q in the Specific Heat Formula?
In the equation:
Q = mcΔT
Q represents the thermal energy transferred to or from the substance.
The SI unit of Q is the joule (J).
If the substance absorbs energy, Q is positive when using the usual sign convention. If the substance loses energy, Q can be treated as negative depending on the problem and sign convention being used.
Units for Specific Heat Capacity
The SI unit for specific heat capacity is:
J/kg·K
It can also be written as:
J/(kg·K)
Specific heat capacity may also be expressed as J/kg·°C when dealing with temperature changes because a temperature difference of 1 K has the same magnitude as a temperature difference of 1°C.
In:
Q = mcΔT
the units are:
- Q = J
- m = kg
- c = J/kg·K
- ΔT = K
How to Find Specific Heat
To find specific heat capacity experimentally, you need to know:
- The thermal energy transferred, Q
- The mass of the substance, m
- The change in temperature, ΔT
Then use:
c = Q/(mΔT)
For example, if a known amount of electrical energy is supplied to a material, the energy can be calculated from:
Q = Pt
where P is power in watts and t is time in seconds.
Substituting this into the specific heat capacity equation gives:
c = Pt/(mΔT)
This provides a method for determining the specific heat capacity of a material in a laboratory.
Values of Common Materials
Different materials have different specific heat capacities.
| Substance | Phase / State | Specific Heat Capacity c (J/kg·K) |
|---|---|---|
| Water | Liquid | 4,186 |
| Ice | Solid | 2,090 |
| Steam | Gas | 2,010 |
| Aluminum | Solid | 900 |
| Concrete | Solid | 880 |
| Glass | Solid | 840 |
| Iron / Steel | Solid | 450 |
| Copper | Solid | 385 |
| Mercury | Liquid | 140 |
| Lead | Solid | 128 |
These values explain why some substances heat up more quickly than others when the same amount of energy is transferred.
Why Does Water Have Such a High Specific Heat Capacity?
Water has a specific heat capacity of approximately:
4186 J/kg·K
This is relatively high compared with many common metals.
A high specific heat capacity means that a large amount of thermal energy is needed to produce a given temperature increase. This makes water useful as a thermal buffer in cooling systems and natural environments.
Water’s high heat capacity also helps large bodies of water absorb and release thermal energy gradually, reducing rapid temperature changes.
Solved Specific Heat Capacity Examples
Example 1: Heating Water
How much thermal energy is required to raise the temperature of 3 kg of water from 20°C to 100°C?
Given:
m = 3 kg
c = 4186 J/kg·K
ΔT = 100 − 20 = 80°C
Formula:
Q = mcΔT
Calculation:
Q = (3)(4186)(80)
Q = 1,004,640 J
Therefore:
Q = 1,004.64 kJ
Example 2: Finding Temperature Rise
An electrical heater transfers 800 J of thermal energy to a 0.4 kg copper block. The specific heat capacity of copper is 385 J/kg·K. Find the temperature rise.
Given:
Q = 800 J
m = 0.4 kg
c = 385 J/kg·K
Formula:
ΔT = Q/(mc)
Calculation:
ΔT = 800/(0.4 × 385)
ΔT = 800/154
ΔT ≈ 5.19°C
Therefore:
ΔT ≈ 5.19°C
Example 3: Finding Specific Heat Capacity
A 2 kg block of an unknown material absorbs 6000 J of thermal energy. Its temperature increases from 25°C to 100°C. Find its specific heat capacity.
Given:
Q = 6000 J
m = 2 kg
ΔT = 100 − 25 = 75°C
Formula:
c = Q/(mΔT)
Calculation:
c = 6000/(2 × 75)
c = 6000/150
c = 40 J/kg·K
Therefore:
c = 40 J/kg·K
The result represents the specific heat capacity calculated for the sample.
Heat Capacity and Specific Heat Capacity Formula
Heat capacity and specific heat capacity are related but describe different quantities.
The heat capacity formula is:
C = Q/ΔT
For an object with mass m:
C = mc
Heat capacity is measured in J/K.
The specific heat capacity formula is:
c = Q/(mΔT)
Specific heat capacity is measured in J/kg·K.
The important difference is that heat capacity describes the thermal capacity of the whole object, while specific heat capacity describes the thermal capacity per unit mass of the material.
What Is Latent Heat?
Latent heat is the thermal energy transferred during a change of state when the temperature remains constant.
Common phase changes include:
- Melting: solid → liquid
- Freezing: liquid → solid
- Vaporization: liquid → gas
- Condensation: gas → liquid
Specific heat capacity is used when the temperature changes without a change of state.
Latent heat is used when the substance changes state without a temperature change.
Specific Latent Heat Formula: Q = mL
The specific latent heat formula is:
Q = mL
This is also commonly called the SLH equation.
Where:
- Q = thermal energy transferred in joules (J)
- m = mass in kilograms (kg)
- L = specific latent heat in J/kg
To find specific latent heat:
L = Q/m
To find mass:
m = Q/L
Specific Latent Heat of Fusion and Vaporization
There are two common types of specific latent heat.
Specific latent heat of fusion (Lf) is the energy required to change 1 kg of a substance between solid and liquid without changing its temperature.
Specific latent heat of vaporization (Lv) is the energy required to change 1 kg of a substance between liquid and gas without changing its temperature.
Specific Heat Capacity and Specific Latent Heat
The two quantities can be distinguished using their formulas:
| Quantity | Formula | Describes | Unit |
|---|---|---|---|
| Specific heat capacity | Q = mcΔT | Temperature change | J/kg·K |
| Specific latent heat | Q = mL | Change of state | J/kg |
A simple way to remember the difference is:
Temperature changes → Q = mcΔT
State changes → Q = mL
Latent Heat Values
| Substance | Latent Heat of Fusion Lf (kJ/kg) | Latent Heat of Vaporization Lv (kJ/kg) |
|---|---|---|
| Water | 334 | 2,260 |
| Ethanol | 108 | 841 |
| Lead | 24.7 | 871 |
| Nitrogen | 25.7 | 198 |
Latent Heat Worked Example
How much thermal energy is required to completely melt 2 kg of ice at 0°C into liquid water at 0°C?
Given:
m = 2 kg
Lf = 334,000 J/kg
Formula:
Q = mLf
Calculation:
Q = (2)(334,000)
Q = 668,000 J
Therefore:
Q = 668 kJ
The temperature remains at the melting point during this phase change.
Thermal Equilibrium and Method of Mixtures
When hot and cold substances are mixed in an insulated system, thermal energy is conserved.
The heat lost by the hot substance equals the heat gained by the cold substance:
Heat Lost = Heat Gained
For two substances:
m₁c₁(T₁ − Tf) = m₂c₂(Tf − T₂)
where Tf is the final equilibrium temperature.
Mixed Water Equilibrium Example
500 g (0.5 kg) of hot water at 80°C is mixed with 300 g (0.3 kg) of cold water at 20°C. Calculate the final equilibrium temperature.
Because both samples are water, their specific heat capacities are the same and cancel:
0.5(80 − Tf) = 0.3(Tf − 20)
Expand:
40 − 0.5Tf = 0.3Tf − 6
Therefore:
46 = 0.8Tf
Tf = 46/0.8
Tf = 57.5°C
Therefore, the final equilibrium temperature is:
57.5°C
For an interactive demonstration of energy exchange and heating, see the PhET Energy Forms and Changes Simulation.
Real-World Applications of Specific Heat Capacity
Specific heat capacity is important in many practical situations.
- Water cooling systems: Water can absorb substantial thermal energy because of its high specific heat capacity.
- Automotive radiators: Cooling systems use fluids with suitable thermal properties to transfer heat away from engines.
- Climate moderation: Large bodies of water absorb and release thermal energy, helping reduce rapid temperature changes.
- Cookware: Materials are selected according to their thermal properties and how quickly they heat and transfer energy.
- Thermal engineering: Specific heat capacity is used when designing heating, cooling, and insulation systems.
When Should You Use Specific Heat Capacity?
Specific heat capacity is used when you need to determine how much thermal energy is required to change the temperature of a material, or when you need to calculate its temperature change, mass, or specific heat capacity. It is commonly applied in school and college physics problems, laboratory experiments, thermal engineering, cooling systems, automotive applications, cookware design, and climate studies. In practical decision-making, specific heat capacity helps engineers and scientists compare materials and choose substances that can absorb, store, or transfer thermal energy effectively.
For additional physics study resources, see the Mechanics hub and free PDF notes.
High Specific Heat Capacity of ocean water moderating coastal climate
Frequently Asked Questions
What is the formula for specific heat capacity?
The main formula is:
Q = mcΔT
To calculate specific heat capacity directly:
c = Q/(mΔT)
What is the specific heat formula in physics?
The specific heat formula used in thermal physics is:
Q = mcΔT
Here, Q is thermal energy, m is mass, c is specific heat capacity, and ΔT is the change in temperature.
How do you find specific heat?
To find specific heat capacity, divide the thermal energy transferred by the product of mass and temperature change:
c = Q/(mΔT)
You need to know Q, m, and ΔT.
What is Q in the specific heat capacity formula?
In:
Q = mcΔT
Q represents the thermal energy transferred. Its SI unit is the joule (J).
What are the units for specific heat capacity?
The SI unit of specific heat capacity is:
J/kg·K
It may also be written as J/kg·°C when referring to a temperature change.
What is the specific latent heat formula?
The specific latent heat formula is:
Q = mL
To find specific latent heat:
L = Q/m
The SI unit of specific latent heat is J/kg.
What is the difference between specific heat and latent heat?
Specific heat capacity describes energy transferred when the temperature changes.
Latent heat describes energy transferred during a change of state while temperature remains constant.
For temperature changes:
Q = mcΔT
For phase changes:
Q = mL
What is the relationship between heat capacity and specific heat capacity?
Heat capacity is:
C = Q/ΔT
For an object of mass m:
C = mc
Specific heat capacity is:
c = Q/(mΔT)
Therefore, heat capacity is the total thermal capacity of an object, while specific heat capacity is the thermal capacity per unit mass.
How is specific heat capacity measured in a laboratory?
Specific heat capacity can be measured by supplying a known amount of thermal energy to a sample and measuring its mass and temperature change.
For electrical heating:
Q = Pt
Therefore:
c = Pt/(mΔT)
where P is the heater’s power and t is the heating time.
Specific Heat Capacity Formula Summary
For quick revision, the key equations are:
Specific heat capacity:
Q = mcΔT
Finding specific heat capacity:
c = Q/(mΔT)
Finding temperature change:
ΔT = Q/(mc)
Heat capacity:
C = Q/ΔT = mc
Specific latent heat:
Q = mL
Finding specific latent heat:
L = Q/m
These formulas provide the foundation for solving specific heat capacity, heat transfer, thermal equilibrium, and latent heat problems in physics.