When people exercise, they report feeling exhaustion when their body temp rises to 39.7 C a 68 kg man is running at 15 km/h on a hot muggy day that he cant lose any heat to the environment his body temp starts at 37 Chow long can he run til he feels exhaustion

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:

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:

P = 862.5 W

Using the relation of Power to heat, we have:

By making time (t) the subject, we can now determine how long he runs till he feels exhausted.

∴

time (t) ≅ 745 s

Learn more about the specific heat of a substance here:

link

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

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