If a human needs to eat about 10 000 kJ per day, estimate (to the nearest gram) the mass of phytoplankton that would be required to meet their daily
energy requirements. Based on this value, approximately what proportion of her own body weight in phytoplankton would a 60 kg woman need to eat over the course of a year, if this were her only source of energy? Show workings please. cheers.
To estimate the mass of phytoplankton required to meet a human's daily energy requirements, we need to know the energy content of phytoplankton. Typically, the energy content of phytoplankton is given in terms of Calories rather than kilojoules. Therefore, we will convert the energy requirement from kilojoules to Calories.
1 joule (J) = 0.239005736 Calories (cal)
1 Calorie (Cal) = 1000 calories (cal)
So, 10,000 kJ (kilojoules) = 10,000 / 0.239005736 = 41,851.88 Calories
Next, we need to find the energy content of phytoplankton. The average energy content of phytoplankton is estimated to be around 1.5 calories per gram.
So, to determine the mass of phytoplankton required, we divide the energy requirement (41,851.88 Calories) by the energy content per gram (1.5 calories per gram):
Mass of phytoplankton required = 41,851.88 / 1.5 = 27,901.25 grams or 27.9 kg (rounded to the nearest gram)
Now, to calculate the proportion of her own body weight that the 60 kg woman would need to eat over the course of a year, we need to determine the total amount of phytoplankton she would consume.
Assuming she eats only phytoplankton for her energy needs, and eats the daily requirement consistently throughout the year, we can calculate the total mass of phytoplankton she would consume annually:
Total phytoplankton consumption = Mass of phytoplankton required per day (27.9 kg) x Number of days in a year
Total phytoplankton consumption = 27.9 kg/day x 365 days = 10,153.5 kg (rounded to the nearest gram)
Finally, we can calculate the proportion of her own body weight:
Proportion of body weight = Total phytoplankton consumption / Body weight
Proportion of body weight = 10,153.5 kg / 60 kg = 169.23 (rounded to two decimal places)
Therefore, a 60 kg woman would need to eat approximately 169.23 times her own body weight in phytoplankton over the course of a year if phytoplankton were her only source of energy.