Question

A runner has a body weight of 65 kg and a core body temperature of 37°C at re&t. The runner performs a 50 minute run at 15 kcal per minute. If the runner is 30% efficient and can only lose 65% of heat produced during running, what is their

new core body temperature? (The specific heat value for the human body is 0.83 kcal).

Answer 1

The runner's new core body temperature after a 50-minute run at 15 kcal per minute, with 30% efficiency and 65% heat loss, is approximately 37.8°C.

Step-by-step explanation:

During the 50-minute run, the runner expends a total of 50 minutes * 15 kcal/minute = 750 kcal. With 30% efficiency, only 30% of the total energy expended contributes to useful work, which is 0.3 * 750 kcal = 225 kcal.

The remaining 70% of energy is dissipated as heat, which is 0.7 * 750 kcal = 525 kcal. Since the runner can only lose 65% of the produced heat, the effective heat loss is 0.65 * 525 kcal = 341.25 kcal.

The body's specific heat is 0.83 kcal, so the change in core body temperature can be calculated using the formula:

`\[ \text{Change in temperature} = \frac{\text{Heat loss}}{\text{Body weight} * \text{Specific heat}} \]`

Substituting the values, we get:

Change in temperature =
`\frac{341.25 \, \text{kcal}}{65 \, \text{kg} * 0.83 \, \text{kcal/°C}}` ≈ 6.03°C

Adding this change to the initial core body temperature:

New core body temperature = 37°C + 6.03°C ≈ 37.8°C

Therefore, the runner's new core body temperature is approximately 37.8°C after the run.