Our bodies can use glucose, C6H12O6 (s) (MM = 180.2 g/mol ) , as a fuel. The heat of combustion

of glucose in 2.820 x 103 kJ/mol. The human body has a specific heat of 4.18 J·˚C−1·g−1

Howmany grams of glucose would an 80.0 kg person need to consume to raise the body temperature
from 36.0 to 39.0 ºC? Assume that all energy goes to warm the body.

Let assume mass of glucose consumed as Mg converting to moles give:M/180.2moles.so the heat energy released by oxidation of this amount of glucose is:M/180.2*2.82*10^6JThis heat cause the temp rise of 3celsius. 15649.2M=80*4180*3 M=64.1Kg

To calculate the amount of glucose needed to raise the body temperature from 36.0 to 39.0 ºC, we need to determine the amount of energy required for this temperature change. We can then relate this energy to the heat of combustion of glucose to find the mass of glucose needed.

First, let's calculate the energy required to raise the body temperature using the mass, specific heat, and temperature difference formula:

Energy = mass x specific heat x temperature difference

Since we are given the specific heat of the human body as 4.18 J·˚C−1·g−1, the temperature difference is (39.0 - 36.0) ºC = 3.0 ºC, and the mass of the person is 80.0 kg, we can plug in these values:

Energy = 80.0 kg x 4.18 J·˚C−1·g−1 x 3.0 ºC

Now, we need to convert the energy from kilojoules to joules to match the units of the heat of combustion of glucose, which is given in kJ/mol. We can achieve this by multiplying the value by 1000:

Energy = 80.0 kg x 4.18 J·˚C−1·g−1 x 3.0 ºC x 1000 (to convert kJ to J)

Now, we have the energy required in joules. Next, we can use the heat of combustion of glucose to determine the mass of glucose needed. The heat of combustion of glucose is given as 2.820 x 103 kJ/mol. We need to relate the energy to the number of moles of glucose and then convert moles to grams by using the molar mass.

To calculate the number of moles of glucose, divide the energy in joules by the heat of combustion in joules per mole:

Moles of glucose = Energy / heat of combustion

Moles of glucose = (80.0 kg x 4.18 J·˚C−1·g−1 x 3.0 ºC x 1000) / (2.820 x 103 kJ/mol x 1000 J/1 kJ)

Finally, to obtain the mass of glucose needed, multiply the number of moles by the molar mass of glucose:

Mass of glucose = Moles of glucose x molar mass of glucose

The molar mass of glucose is given as 180.2 g/mol. Substitute the value of moles of glucose into the equation:

Mass of glucose = Moles of glucose x 180.2 g/mol

By following these steps, you should be able to calculate the mass of glucose required for a person to raise their body temperature from 36.0 ºC to 39.0 ºC.