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Fever, or pyrexia, is the body's natural response to infection, leading to an increase in the body's setpoint temperature. This was one of the most common symptoms experienced by people infected with the COVID-19 virus during the pandemic in 2020. Normal body temperature was recently established to be 97.9 °F (36.6 °C), and during a high fever, the body temperature may rise to 103 °F (39.4 °C) or more. This heat is produced by the body ramping up its metabolic rate and burning more calories.

How many calories would a 75.0-kg person have to consume in order to raise their temperature from 36.6 °C to 39.4 °C? Take the average specific heat capacity of the human body to be 3470 J/(kg⋅°C).

Number: _______
Units: _______

Answer :

Final answer:

To calculate the amount of calories required to raise the body temperature of a 75.0-kg person from 36.6 °C to 39.4 °C, we need to use the formula Q = mcΔT where Q is the energy in joules, m is the mass in kg, c is the specific heat capacity in J/(kg·C), and ΔT is the change in temperature in °C. By plugging in the given values, we can find that the person would need to consume approximately 172,789 calories.

Explanation:

To calculate the amount of calories required to raise the body temperature of a 75.0-kg person from 36.6 °C to 39.4 °C, we can use the formula:

Q = mcΔT

Where:
Q is the energy in joules
m is the mass in kg
c is the specific heat capacity in J/(kg·C)
ΔT is the change in temperature in °C

First, we need to calculate the energy in joules using the given values:
m = 75.0 kg
c = 3470 J/(kg·C)
ΔT = 39.4 °C - 36.6 °C = 2.8 °C

Plugging these values into the equation gives:

Q = (75.0 kg)(3470 J/(kg·C))(2.8 °C) = 721,850 J

Next, we can convert the energy in joules to calories using the conversion factor:
1 cal = 4.184 J

Therefore, the number of calories required would be:

(721,850 J) / (4.184 J/cal) = 172,789 cal

So a 75.0-kg person would need to consume approximately 172,789 calories to raise their temperature from 36.6 °C to 39.4 °C.

Learn more about Calculating Calories to Raise Body Temperature here:

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