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BIO While running, a 70-kg student generates thermal energy at a rate of 1200 W. For the runner to maintain a constant body temperature of 37\(^\circ\)C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the energy could not flow out of the student’s body, for what amount of time could a student run before irreversible body damage occurred? (Note: Protein structures in the body are irreversibly damaged if body temperature rises to 44\(^\circ\)C or higher. The specific heat of a typical human body is 3480 J / kg \(\cdot\) K, slightly less than that of water. The difference is due to the presence of protein, fat, and minerals, which have lower specific heats.)

Short Answer

Expert verified
The student can run for about 23.6 minutes before body damage occurs.

Step by step solution

01

Identify the Known Values

First, list all the known values from the problem:- Mass \( m = 70 \text{ kg} \)- Power generated \( P = 1200 \text{ W} \)- Initial temperature \( T_i = 37\degree{C} \)- Final temperature \( T_f = 44\degree{C} \)- Specific heat \( c = 3480 \text{ J/kg} \cdot K \).
02

Determine Temperature Change

Calculate the change in temperature \( \Delta T \) using the temperature values:\[ \Delta T = T_f - T_i = 44\degree{C} - 37\degree{C} = 7\degree{C} \]
03

Calculate Energy Required for Temperature Change

Use the specific heat formula \( Q = mc\Delta T \) to calculate the energy required to raise the body's temperature:\[ Q = m \times c \times \Delta T = 70 \times 3480 \times 7 = 1,700,400 \text{ J} \]
04

Calculate Time Until Irreversible Damage

Determine the time \( t \) it takes for the energy to reach \( Q \) using power with \( Q = P \times t \):\[ t = \frac{Q}{P} = \frac{1,700,400}{1200} \approx 1417 \text{ seconds} \].Convert seconds to minutes for easier interpretation:\[ 1417 \text{ seconds} \div 60 \approx 23.6 \text{ minutes} \]
05

Conclusion

The student can run for approximately 23.6 minutes before the body temperature reaches the critical level that might cause irreversible damage.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Specific Heat Capacity
Specific heat capacity is an essential concept in understanding how much heat energy it takes to change the temperature of a substance. Specifically, it refers to the amount of heat needed to raise the temperature of one kilogram of a material by one degree Celsius or Kelvin.

In this exercise, we observed that the specific heat capacity of the human body is 3480 J/kg·K. This means that to increase one kilogram of body mass by 1°C, 3480 Joules of energy are required. This value is close to but lower than the specific heat of water, due to the presence of proteins and fats which have additional thermal properties.

Understanding the specific heat capacity helps us determine how rapidly or slowly a body can heat up, which is crucial for athletes and people engaged in physical activities. The higher the specific heat, the more energy is needed to increase temperature, affecting how the human body absorbs and dissipates heat during various conditions.
Body Temperature Regulation
The human body has evolved with several mechanisms for maintaining its core temperature around 37°C, regardless of external conditions. This process, known as thermoregulation, involves balancing heat production with heat loss.

During physical activities such as running, the body generates more heat. To prevent overheating, it must eliminate this extra thermal energy through various methods like sweating or increased blood flow to the skin. These mechanisms help maintain the core body temperature within a safe range.

In the absence of these cooling methods, like in our exercise example, the body could potentially heat up to dangerous levels (44°C in this case). When this happens, proteins and enzymes may denature, leading to life-threatening conditions. Thus, the ability to regulate body temperature effectively is vital for health and performance.
Thermal Energy Transfer
Thermal energy transfer in biological systems occurs through various mechanisms to maintain a stable internal environment. Heat can move by conduction, convection, and radiation, all of which play roles in how the body cools down or warms up in different situations.

In the given scenario, thermal energy is generated at a rate of 1200 watts while running. If not efficiently dissipated, this energy could accumulate, raising body temperature towards the critical level.
The process of transferring heat away can include:
  • Perspiration: Sweat evaporates from the skin surface, a process that absorbs heat energy and cools the body.
  • Blood Flow: Increased circulation brings warmer blood to the cooler surface of the skin.
  • Breathing: Exhaling warmer air and inhaling cooler air aids in heat loss.
These processes rely on the effective exchange of thermal energy, ensuring the body does not overheat during intense activities.

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Most popular questions from this chapter

A U.S. penny has a diameter of 1.9000 cm at 20.0\(^\circ\)C. The coin is made of a metal alloy (mostly zinc) for which the coefficient of linear expansion is \(2.6 \times 10{^-}{^5} K{^-}{^1}\). What would its diameter be on a hot day in Death Valley (48.0\(^\circ\)C)? On a cold night in the mountains of Greenland (-53\(^\circ\)C)?

(a) Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other. (b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other.

Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon (400 K); (b) the temperature at the tops of the clouds in the atmosphere of Saturn (95 K); (c) the temperature at the center of the sun \((1.55 \times 10{^7} K)\).

Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the values in the table? Assume that all values other than the specific heat (solid) are correct. The actual time (a) will be shorter; (b) will be longer; (c) will be the same; (d) depends on the density of the cryoprotectant.

BIO Treatment for a Stroke. One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0\(^\circ\)C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached 32.0\(^\circ\)C. To treat a 70.0-kg patient, what is the minimum amount of ice (at 0°C) you need in the bath so that its temperature remains at 0°C? The specific heat of the human body is 3480 J/kg \(\cdot\) C\(^\circ\), and recall that normal body temperature is 37.0\(^\circ\)C.

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