While jogging, a 70.0-kg student generates thermal energy at a rate of 1200 W. To maintain a...

Question:

While jogging, a 70.0-kg student generates thermal energy at a rate of 1200 W. To maintain a constant body temperature of 37.0 {eq}^\circ {/eq}C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the heat could not flow out of the student's body, irreversible body damage could occur. Protein structures in the body are irreversibly damaged if body temperature rises to 44.0 {eq}^\circ {/eq}C or above. The specific heat of a typical human body is 3480J/(kg*K), slightly less than that of water. (The difference is due to the presence of protein, fat, and minerals, which have lower specific heat capacities.) For how long a time t could a student jog before irreversible body damage occurs?

Thermal Energy:

Energy can be expressed as the product of power and time. For the energy removed by perspiration, it can also be expressed as the total thermal energy of the human body. This thermal energy is equal to the product of the mass of the body, the specific heat capacity, and the change in temperature.

Answer and Explanation:

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Let the energy of the student be:

{eq}E = Q = mc\Delta T {/eq}

Where, we can have the energy on the left side in terms of the power.

{eq}Pt =...

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