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Heat Transfer Equations

Last Updated : 23 Jul, 2025
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Heat is a type of energy that moves from a hot thing to a cold thing. When we make contact with something cold, heat from our bodies is transferred to the cold item. Heat is transferred between objects of differing temperatures. The passage of heat ceases when the two objects reach the same temperature.

Heat Transfer

Heat transfer occurs when energy from a higher-temperature body transfers to a lower-temperature body. Heat is the term for the energy in transit. Our palms feel cold when we hold an ice cube in our hands. This occurs as a result of heat transmission from our bodies to the ice cube. The temperature of our hands drops as a result of the loss of heat from our bodies, making us feel chilly. The faster heat transfer happens between two items, the greater the temperature differential between them.

Heat Transfer Formula

Q = C×m×ΔT

Where,

Q = heat

c = specific heat

m = mass of the body

ΔT = temperature difference

The transfer of heat occurs by three different processes , which are ,

1. Conduction

2. Convection

3. Radiation

1. Conduction

Conduction of heat is the transfer of thermal energy through a material from high temperature to low temperature, without the movement of the material itself.

Heat transfer by the process of conduction can be expressed as ,

Q = kA ( T Hot- T Cold ) t/d

Where,

Q = Heat transferred (Joules)

k = Thermal conductivity of the material (W/m·K)

A = Cross-sectional area through which heat is transferred (m²)

( T Hot- T Cold )= Temperature difference between the two ends (K or °C)

d = Thickness of the material (m)

2. Convection

Convection of heat is the transfer of thermal energy through a fluid (liquid or gas) by the movement of the fluid itself, typically due to temperature differences.

Heat transfer by the process of convection can be expressed as ,

Q = HcA ( T Hot- T Cold )

Here, Hc is the heat transfer coefficient.

3. Radiation

Radiation of heat is the transfer of thermal energy through electromagnetic waves, without the need for a medium, allowing heat to travel through a vacuum.

Heat transfer by the process of Radiation can be expressed as ,

Q = σ(T4Hot - T4Cold) A

Here 'σ' is known as Stefan Boltzmann Constant.

Solved Examples

1. Determine the heat needed to raise a 1 kg of iron from 250° C to 600° C?

Mass, m = 1 Kg,
Specific heat of iron, C = 0.45 Jg−1°C
Also, temperature difference,
ΔT=700°C–250°C
ΔT=450°C
Now applying the heat formula,
c=Q/mΔT
Rearranging the formula
Q=mcΔT
Q=1×0.45×103×450
= 20.25 J

2. Determine how much heat energy is lost if 50 Kg water is cooled from 600\degree C to 200\degree C. Specific heat of water is given as C=4.2×103JKg−1°C.

Mass of water, m = 50 Kg,
Specific heat of water, C = 4.2×103JKg−1°
Temperature difference,
ΔT=–40°
Heat energy by formula is,
Q = mcΔT
Q = 50×4.2×103×(−400)
Q= – 840 J

3. A system weighing 5 Kgs is heated from its initial temperature of 30ᵒC to its final temperature of 60ᵒC. Calculated the total heat gained by the system. (Specific heat of the system = 0.45 kJ/Kg K)

The Initial temperature of the system, Ti = 30ᵒC
The Final temperature of the system, Tf = 60ᵒC
Mass of the system, m = 5 kg
The total heat gained by the system can be calculated by using the formula for heat transfer as mentioned above,
Q= c x m x ΔT
Q=5×0.45×30
Q=67.5 J

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