The oxygen taken in by the body reacts with fats, carbohydrates, and protein, liberating energy internally at a rate of about 2.12×104 J /liter. If a 85.4 kg man requires 73.0 W of power even while sleeping, what is his rate of oxygen consumption?

To calculate the rate of oxygen consumption, we can use the equation:

Rate of oxygen consumption = Power / Energy liberated per liter

Given:
Power (P) = 73.0 W
Energy liberated per liter (E) = 2.12x10^4 J/L

Substituting these values into the equation, we have:

Rate of oxygen consumption = 73.0 W / (2.12x10^4 J/L)

Now we can calculate the rate of oxygen consumption.

To determine the rate of oxygen consumption by the man, we can use the power requirement and the energy liberation rate per unit volume.

Given:
- Energy liberation rate per unit volume (ε) = 2.12 × 10^4 J/liter
- Power requirement (P) = 73.0 W

First, we need to find the volume of oxygen consumed per second (V) by the man. We can use the formula:

Power (P) = Energy (ε) × Volume (V) × Time (t)

Rearranging the formula:
V = P / (ε × t)

To find the rate of oxygen consumption, we need to define a specific time interval. Assuming that the power requirement is constant and the time interval is 1 second:

V = P / ε

Next, we need to convert the mass of the man (85.4 kg) to volume. One liter of pure water has a mass of 1 kg, so the volume of the man can be estimated as 85.4 liters.

Finally, we can calculate the rate of oxygen consumption:

Rate of oxygen consumption = V × Volume of the man

Rate of oxygen consumption = (P / ε) × 85.4 liters

Substituting the given values:
Rate of oxygen consumption = (73.0 W) / (2.12 × 10^4 J/liter) × 85.4 liters

Using a calculator:
Rate of oxygen consumption ≈ 0.306 liters/second

Therefore, the rate of oxygen consumption by the man while sleeping is approximately 0.306 liters/second.