Problem — Fermi estimate: power of a human being

Fermi estimate: power of a human being. Given that average metabolic consumption is $\sim 2000$ kcal/day $\sim 8{,}4\;\mathrm{MJ}$/day, estimate the average power of a human being in normal activity. Compare with a household appliance and give the order of magnitude of sporting peaks.

Solution

Data: daily energy $E \approx 8{,}4\;\mathrm{MJ} = 8{,}4\cdot 10^6\;\mathrm{J}$; duration of one day $t = 24\cdot 3600 = 86\,400\;\mathrm{s}$.

Average power (energy divided by time):

$P = \frac{E}{t} = \frac{8{,}4\cdot 10^6}{86\,400} \approx 97\;\mathrm{W}$

$\ev{P \approx 97\;\mathrm{W}}$

Comparison. About $100\;\mathrm{W}$: the power of an old incandescent light bulb. A human body at rest or in light activity radiates into the environment roughly the same energy as a lit bulb — which is why a room full of people warms up noticeably.

Sporting peaks. In an intense, brief effort (a sprint, a cycling breakaway) an athlete can deliver much greater power, of the order of $\sim 10^3\;\mathrm{W}$ (a few hundred up to over a thousand watts at peak). But this cannot be sustained for long: the daily average remains around $\sim 100\;\mathrm{W}$.

Physical reading. The estimate places human beings on an intuitive power scale ($\sim 10^2\;\mathrm{W}$) and shows the gap between sustainable average power and peak power (a factor of $\sim 10$), a central theme in the physiology of effort.

Collegamenti

Argomenti: Work and energy Concetti: Power Competenze: Fermi estimates