Question

A pronghorn antelope can run at a remarkable 18 m/sm/s for up to 10 minutes, almost triple the speed that an elite human runner can maintain. for a 32 kgkg pronghorn, this requires an astonishing 3.4 kwkw of metabolic power, which leads to a significant increase in body temperature. If the pronghorn had no way to exhaust heat to the environment, by how much would its body temperature increase during this run? (In fact, it will lose some heat, so the rise won't be this dramatic, but it will be quite noticeable, requiring adaptations that keep the pronghorn's brain cooler than its body in such circumstances.) Assume the efficiency of the pronghorn to be equal to that of human.

Express your answer in kelvin.

Answer 1

The body temperature of a pronghorn antelope would increase by approximately 0.031°C during a run if it had no way to exhaust heat.

Step-by-step explanation:

The body temperature of a pronghorn antelope would increase significantly during its run if it had no way to exhaust heat to the environment. To calculate the increase in body temperature, we can use the formula:

ΔT = P/(mC),

where ΔT is the change in temperature, P is the power required, m is the mass, and C is the specific heat capacity of the pronghorn.

Given that the power required is 3.4 kW, the mass is 32 kg, and the specific heat capacity of the pronghorn is approximately the same as humans (assuming 3.45 kJ/kg°C), we can substitute these values into the formula to find the change in temperature.

ΔT = 3.4 kW/(32 kg * 3.45 kJ/kg°C) = 0.031°C

Therefore, if the pronghorn had no way to exhaust heat, its body temperature would increase by approximately 0.031°C during the run.