Because water is a much more efficient thermal conductor than air, marine mammals often have thick layers of blubber (under-skin fat, with a thermal conductivity of 0.250 W/(m °C)) and a small surface-to-volume ratio to minimize the loss of energy by heat to the surrounding water. The beluga whale, Delphinapterus leucas, is a species of whale native to the Arctic and sub-Arctic regions. The core body temperature of this whale is usually 37.0°C, and its basal metabolic rate (BMR) is 7.30 x 104 kJ/day. The beluga often finds itself near the Arctic ice sheet, where the water temperature is very close to 0°C. (a) Modeling the body of the whale as a cylinder of length h = 4.10 m and diameter d = 1.20 m,estimate the average thickness (in cm) of the beluga's blubber required to keep the core temperature of the whale fixed at 37.0°C. (For simplicity, treat the blubber layer on the lateral cylindrical surface as a rectangular slab with a constant area. Take the front and rear surfaces of the cylinder into account as well. Assume any energy transfer is due only to conduction.) cm (b) In a given day, the beluga whale often swims from the cold waters near the Arctic ice sheet to waters as warm as 15.0°C. In these warmer waters, the rate of thermal conduction into the surrounding water will be less than the BMR, and the whale's core body temperature could increase. What power (in W) must be expended as mechanical work by the whale to keep its core body temperature constant? (Assume that any excess power produced at the basal metabolic rate not required for thermal regulation can be expended as mechanical work.) W

Because water is a much more efficient thermal conductor than air, marine mammals often have thick layers of blubber (under-skin fat, with a thermal conductivity of 0.250 W/(m °C)) and a small surface-to-volume ratio to minimize the loss of energy by heat to the surrounding water. The beluga whale, Delphinapterus leucas, is a species of whale native to the Arctic and sub-Arctic regions. The core body temperature of this whale is usually 37.0°C, and its basal metabolic rate (BMR) is 7.30 x 104 kJ/day. The beluga often finds itself near the Arctic ice sheet, where the water temperature is very close to 0°C. (a) Modeling the body of the whale as a cylinder of length h = 4.10 m and diameter d = 1.20 m,estimate the average thickness (in cm) of the beluga's blubber required to keep the core temperature of the whale fixed at 37.0°C. (For simplicity, treat the blubber layer on the lateral cylindrical surface as a rectangular slab with a constant area. Take the front and rear surfaces of the cylinder into account as well. Assume any energy transfer is due only to conduction.) cm (b) In a given day, the beluga whale often swims from the cold waters near the Arctic ice sheet to waters as warm as 15.0°C. In these warmer waters, the rate of thermal conduction into the surrounding water will be less than the BMR, and the whale's core body temperature could increase. What power (in W) must be expended as mechanical work by the whale to keep its core body temperature constant? (Assume that any excess power produced at the basal metabolic rate not required for thermal regulation can be expended as mechanical work.) W