Final answer:
To address the needs of a mountain climber using oxygen, calculations involve the doubled consumption rate under harsh conditions, the work done against gravity, and the efficiency based on energy expenditure.
Step-by-step explanation:
Calculations for Mountain Climbing with Bottled Oxygen:
Addressing a mountain climber's oxygen needs at high altitudes requires understanding the rate of oxygen consumption and the efficiency of oxygen utilization.
(a) If a climber uses oxygen at twice the standard rate due to harsh conditions, to calculate the amount needed for 10 hours of climbing, we take the normal consumption rate for climbing 116 stairs per minute and double it. Since 40% of the inhaled oxygen is utilized, we must take that into account to ensure the climber has enough to last the duration.
(b) To calculate the useful work done by the climber, one would use the formula for work, which involves the mass of the climber and equipment and the height gained. As the climber ascends, the work done against Earth's gravitational field can be quantified.
(c) The efficiency of the climber for the 10-hour climb is a percentage that relates the useful work accomplished to the total energy expenditure, which includes the oxygen consumed and the physical effort spent during the climb.