Answer :
Final answer:
To raise a 75.0 kg person's body temperature from 36.6°C to 39.4°C, approximately 175,644 calories of energy are required, which translates to about 176 dietary calories (kcal).
Explanation:
To calculate how many calories a 75.0 kg person would need to consume to raise their body temperature from 36.6 degrees Celsius to 39.4 degrees Celsius, we need to use the specific heat capacity of the human body and the temperature change. The specific heat capacity of water, which the human body is mostly composed of, is 3,500 J/kg/°C. First, we convert the desired temperature change from Celsius to Kelvin, which is the same for these purposes, so we have a change of 2.8°C. Then we use the formula:
Q = mcΔT
where Q is the heat in joules, m is the mass in kilograms, c is the specific heat capacity in J/kg/°C, and ΔT is the change in temperature in degrees Celsius.
Plugging in the values: Q = 75.0 kg * 3,500 J/kg/°C * 2.8°C = 735,000 J
Since 1 calorie (cal) is equal to 4.184 joules (J), we divide the total energy in joules by 4.184 J/cal to find the calories:
Q = 735,000 J / 4.184 J/cal ≈ 175,644 cal
The person would need to consume approximately 175,644 calories to raise their body temperature by 2.8°C. However, 1 dietary calorie (kcal) is equal to 1,000 physical calories (cal), so in terms of dietary calories, the person would need approximately 176 kcal.