1. Basic Energy Balance EquationThe total energy relationship in the human body can be expressed as:
E_{in} = W + E_{loss}
Where:
(E_{in}) = Energy intake (from food, in Joules or Calories)
(W) = Useful work done (mechanical or mental work)
(E_{loss}) = Energy lost (heat, friction, inefficiency)
Rearranging:
[
E_{loss} = E_{in} - W
]
2. Efficiency of Human BodyEfficiency tells us how much of the energy is actually used for useful work:
\eta = \frac{W}{E_{in}} \times 100%
Typical human efficiency:
20%–25% for physical work
75%–80% energy is lost as heat and internal inefficiencies
3. Mechanical Work CalculationMechanical work done by the body is:
W = F \times d
Where:
(F) = Force applied (Newtons)
(d) = Distance moved (meters)
Example:If a person lifts a 10 kg weight to a height of 2 meters:
[
F = mg = 10 \times 9.8 = 98 , N
]
[
W = 98 \times 2 = 196 , J
]
So, useful work = 196 Joules
4. Total Energy Used (Metabolic Energy)Suppose the body efficiency is 25%, then:
[
E_{in} = \frac{W}{\eta}
]
[
E_{in} = \frac{196}{0.25} = 784 , J
]
5. Energy Loss Calculation[
E_{loss} = E_{in} - W
]
[
E_{loss} = 784 - 196 = 588 , J
]
So:
Useful work = 196 J
Energy lost = 588 J
👉 This means 75% energy is lost
6. Power Consumption in Human WorkPower is the rate of energy use:
P = \frac{W}{t}
Where:
(P) = Power (Watts)
(t) = Time (seconds)
Example:If the work (196 J) is done in 4 seconds:
[
P = \frac{196}{4} = 49 , W
]
7. Heat Loss ModelMost energy loss is in the form of heat:
[
Q = E_{loss}
]
This heat is dissipated through:
Sweating
Radiation
Convection
8. Energy Loss in Continuous Work (Metabolic Rate)For continuous activity:
[
E = P \times t
]
If a worker uses 200 W power for 1 hour (3600 s):
[
E = 200 \times 3600 = 720,000 , J
]
If efficiency = 25%:
Useful work = 180,000 J
Energy lost = 540,000 J
9. Energy Loss Due to Friction and Internal ResistanceWe can model internal loss as:
[
E_{loss} = E_{heat} + E_{friction} + E_{metabolic}
]
Where:
Heat loss dominates (~70–80%)
Internal friction in muscles and joints contributes additional loss
10. Summary Formula (Complete Model)A more complete representation:
[
E_{loss} = E_{in} - (F \cdot d)
]
or including efficiency:
[
E_{loss} = E_{in} (1 - \eta)
]
Final UnderstandingMathematically, energy loss in the human body during work occurs because:
The body is not 100% efficient
Only ~25% energy becomes useful work
The rest is lost as:
Heat
Internal resistance
Metabolic processes