Respuesta :
Answer:
111 seconds
Explanation:
From research, it takes 4200 J to raise 1 kg of body temperature. Which means that specific heat capacity of human body with is; c = 4200 J/Kg°C
We are told that the temperature starts at 37°C and rises to 39.7°C
Thus: Δt = 39.7 - 37 = 2.7°C
Amount of energy required is given by the formula;
q = mcΔt
We are given m = 68 kg
Thus;
q = 68 × 4200 × 2.7
q = 77112 J
From research, the human body is 25% efficient.
Formula for power with velocity is;
P = F × V
F = mg = 68 × 9.81
V = 15km/h = 4.167 m/s
P = 68 × 9.81 × 4.167
P = 2779.72 W
Since the human body is 25%
Then the power of the utilized is;
25/100 × 2779.72 = 694.93 W
Now, we now that;
Power = work done/time taken
694.93 = 77112/t
t = 77112/694.93
t = 111 seconds.
Thus, it will take home 111 seconds to feel exhausted
The man can run for 745 s till he feels exhausted.
The specific heat is the amount of heat needed to raise the temperature of a 1 gram of a substance by 1° C
Here, the specific heat of the human body is 3500 J / kg /° C
From the information given:
- The initial body temperature = 37° C
- The final body temperature = 39.7° C
- mass of the man running = 68 kg
Here, the heat Q needed is;
Q = mCΔT
Q = 68 × 3500 J/ kg/ ° C × (39.7 -37)° C
Q = 68 × 3500 J/ kg/ ° C × 2.7
Q = 642600 J
At standard conditions, the power value of a man = 1150 W. Suppose 75% of the power is lost to heat.
Then;
Power P becomes:
[tex]\mathbf{P = 1150 \ W \times (\dfrac{75}{100})}[/tex]
P = 862.5 W
Using the relation of Power to heat, we have:
[tex]\mathbf{Power (P) = \dfrac{heat (Q)}{time (t)}}[/tex]
By making time (t) the subject, we can now determine how long he runs till he feels exhausted.
∴
[tex]\mathbf{time (t) = \dfrac{heat (Q)}{Power (P)}}[/tex]
[tex]\mathbf{time (t) = \dfrac{642400 \ J}{ 862.5 W}}[/tex]
[tex]\mathbf{time (t) = 744.81 \ s}[/tex]
time (t) ≅ 745 s
Learn more about the specific heat of a substance here:
https://brainly.com/question/12474790?referrer=searchResults
