n the following problem, consider the human body as a heat engine with efficiency e = 0.2 that can take in energy as food Qh, perform work W, and generate heat Qc. This heat expelled from our muscles (Qc) is an important component of maintaining a constant body temperature, which necessitates a balance of energy intake and output. In order to calculate the energy intake Qh, you will use the table above listing activity factors for selected activities, for a person with a BMR of 1440 kcal/day. For example, the energy required to stand per hour would be (fstand)(BMR) = (1.7)(1440 kcal/day) (1day/24 hours) = 102 kcal/h. For each scenario, calculate the 24 h number of bowls of cereal that must be consumed per hour (1 bowl = 100 kcal) to perform the required activity (Qh) Determine whether you have an energy deficit or surplus by considering the heat generated by your muscles (Qc), the heat loss from conduction, and the heat loss/gain from radiation We will consider heat loss from conduction per hour by assuming that our skin has properties of (thickness = 0.03 m, area = 1.7 m2, thermal conductivity = 0.18 Cal/(m·hr·◦C) and that our skin is maintained at a temperature of 35◦C regardless of the temperature of the environment, and our body temperature is maintained at a temperature of 37◦C. We will also consider heat loss/gain from radiation per hour by assuming that our skin (temperature = 35◦C, area = 1.7 m2, emissivity = 0.7) is emitting heat to AND absorbing heat from the environment. Use σ = 4.88 × 10−8 Cal/(m2 ·hr·K4 ). Technically, we can also consider heat loss/gain from convection, and this can be especially significant in a breezy environment, though we will ignore that here. If you and an energy surplus, calculate the liters of water that must be sweated out to maintain a constant body temperature, using the latent heat of vaporization of water at body temperature to be 580 kcal/L. Pick any two of the following scenarios to analyze: • Walking at a pace of 3 mph in an environment of 47◦C • Running at a pace of 10 mph in an environment of 33◦C • Shivering in an environment of −10◦C

1. In the following problem, consider the human body as a heat engine with efficiency e = 0.2 that can take in energy as food Qh, perform work W, and generate heat Qc. This heat expelled from our muscles (Qc) is an important component of maintaining a constant body temperature, which necessitates a balance of energy intake and output.

   • In order to calculate the energy intake Qh, you will use the table above listing

     activity factors for selected activities, for a person with a BMR of 1440 kcal/day.

     For example, the energy required to stand per hour would be (fstand)(BMR) = (1.7)(1440 kcal/day) (1day/24 hours) = 102 kcal/h. For each scenario, calculate the 24 h number of bowls of cereal that must be consumed per hour (1 bowl = 100 kcal) to perform the required activity (Qh)

   • Determine whether you have an energy deficit or surplus by considering the heat generated by your muscles (Qc), the heat loss from conduction, and the heat loss/gain from radiation

     • We will consider heat loss from conduction per hour by assuming that our skin has properties of (thickness = 0.03 m, area = 1.7 m2, thermal conductivity = 0.18 Cal/(m·hr·◦C) and that our skin is maintained at a temperature of 35◦C regardless of the temperature of the environment, and our body temperature is maintained at a temperature of 37◦C.

     • We will also consider heat loss/gain from radiation per hour by assuming that our skin (temperature = 35◦C, area = 1.7 m2, emissivity = 0.7) is emitting heat to AND absorbing heat from the environment. Use σ = 4.88 × 10−8 Cal/(m2 ·hr·K4 ).

     • Technically, we can also consider heat loss/gain from convection, and this can be especially significant in a breezy environment, though we will ignore that here.

   • If you and an energy surplus, calculate the liters of water that must be sweated out to maintain a constant body temperature, using the latent heat of vaporization of water at body temperature to be 580 kcal/L.

Pick any two of the following scenarios to analyze:

• Walking at a pace of 3 mph in an environment of 47◦C

• Running at a pace of 10 mph in an environment of 33◦C

• Shivering in an environment of −10◦C
• Sitting doing homework in a room at 22◦C