The rise in temperature of the man’s body due to the thermal energy during exercise is [tex]\boxed{9.63\:^{\circ}\text{C}}[/tex] .
Further Explanation:
Given:
The power generated in the body is [tex]1000\,{\text{W}}[/tex] .
The mass of the man is [tex]39\,{\text{kg}}[/tex] .
The time spent by the man on the treadmill is [tex]39\,\min[/tex] .
Concept:
The thermal energy gained by the person while performing exercise may lead to significant increase in the body temperature.
The energy imparted in the person’s body is given by:
[tex]Q={\text{power}}\times{\text{time}}[/tex]
Substitute the value of power and time.
[tex]\begin{aligned}Q&=1000\times\left({39\times60\,\sec}\right)\\&=2340000\,{\text{J}}\\\end{aligned}[/tex]
Now, the specific heat capacity of the human body is estimated to be [tex]3470\text{ J/kg}^{\circ}\text{C}[/tex] .
The heat absorbed by the man’s body can be expressed as:
[tex]Q=m\times C\times\Delta T[/tex]
Here, [tex]m[/tex] is the person’s mass, [tex]C[/tex] is the specific heat capacity of human body and [tex]\Delta T[/tex] is the change in temperature of the body.
Substitute the values in above expression.
[tex]\begin{aligned}2340000&=70\times3470\times\Delta T\\\Delta T&=\dfrac{2340000}{70\times3470}\\&=9.63\:^{\circ}\text{C}\end{aligned}[/tex]
Thus, the rise in temperature of the man’s body due to the thermal energy during exercise is [tex]\boxed{9.63\:^{\circ}\text{C}}[/tex] .
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Answer Details:
Grade: College
Subject: Physics
Chapter: Heat and Thermodynamics
Keywords:
Moderate exercise, increase body temperatures, dangerous levels, metabolic power of 1000 W, thermal energy, couldn’t perspire, runs on a treadmill.
