The energy flux of sunlight hitting the Earth’s surface is roughly 1350 W/m2. As

Question

The energy flux of sunlight hitting the Earth’s surface is roughly 1350 W/m2. As a reminder about units, a Watt (W) is one Joule/second, a Joule is defined to be 1 kg·m2/s2, and there are 4184 Joules in one food calorie.

(a) Assuming a completely sedentary and passive population and considering only energy requirements, estimate the maximum number of people that the Earth can support.

(b) Improve your calculation to (a) by including the fact that each person requires a certain amount of fresh water to survive. Including fresh water requirements, estimate the maximum number of people that the Earth can support. In completing this portion of the problem, you may find it useful to note that the cost of vaporizing water is roughly 2500 Joules/gram; that is, to turn one gram of liquid water into one gram of water vapor, one must supply roughly 2500 Joules of energy.

Explanation / Answer

(a) Given: Flux = 1350 W/m2; Area of earth=1.5x1014 m2

Also we know that ;

Flux=(Watt/m2)   and Watt=(joules/second)

therefore, Watts produced on earth area= 2.025 x 1017 Watts

Joules(Energy) produced in 24 hours and 360 days = (2.025x1017)x (24 x 360) = 1.7496x1022 J

Converting Joules in Calories we get = 4181644359464627200 Kcal

Assuming adult males only, daily minimum calorie intake is 2700 cal (according to US authorities)

Hence, maximum number of people earth can support is   

4181644359464627200000/2700 = 1.5487572x1018

(b) Assuming that all the humans are man

and an average man drinks atleast 3.5 liters daily ie.3500 gm

in a year he drinks 3500x365= 1277500 gm

converting gm to joules = 1277500x2500= 3.19375 x 109 J

converting joules to calorie = 763324.5697897 Kcal.

Hence, maximum number of people earth can support is

(4181644359464627200000)/(763324.5697897000 + 2700)= 5.456744 x 1015

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