Problem 83 - University Physics with Modern Physics

Question

BIO Shivering. Shivering is your body's way of generating heat to restore its internal temperature to the normal 37\(^\circ\)C, and it produces approximately 290 W of heat power per square meter of body area. A 68-kg, 1.78-m-tall woman has approximately 1.8 m\(^2\) of surface area. How long would this woman have to shiver to raise her body temperature by 1.0 C\(^\circ\), assuming that the body loses none of this heat? The body’s specific heat capacity is about 3500 J/kg \(\cdot\) K.

Step-by-Step Solution

Answer

She needs to shiver for about 456 seconds.

Step 1: Calculate Total Heat Required

First, determine the total heat energy required to raise the woman's body temperature by 1.0 C°. Use the formula: \( Q = mc\Delta T \), where \( Q \) is the heat energy, \( m \) is the mass of the woman, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change. Here, \( m = 68 \) kg, \( c = 3500 \) J/kg·K, and \( \Delta T = 1.0 \) C° (or 1.0 K). Thus, \( Q = 68 \cdot 3500 \cdot 1 = 238,000 \) J.

Step 2: Calculate Heat Power Produced by Shivering

Shivering produces 290 W (joules per second) of heat power per square meter of body surface area. Since the woman's body has a surface area of 1.8 m², the total heat power produced is calculated as: \( 290 \cdot 1.8 = 522 \) W.

Step 3: Calculate Shivering Time

To find out how long she needs to shiver, divide the total heat required by the heat power produced. Use the formula: \( \text{time} = \frac{Q}{P} \), where \( Q = 238,000 \) J is the total heat required and \( P = 522 \) W is the power. Thus, \( \text{time} = \frac{238,000}{522} \approx 456 \) seconds.

Key Concepts

Specific Heat Capacity

Specific heat capacity is a fundamental concept in understanding how materials absorb heat. It describes the amount of heat energy required to raise the temperature of a given amount of substance by one degree Celsius (or one Kelvin). This property varies between different substances. For instance, water has a high specific heat capacity, meaning it requires more energy to change its temperature compared to metals, which have a low specific heat capacity.
In the context of the exercise, the specific heat capacity of the human body is approximately 3500 J/kg·K. This means that it takes 3500 joules of energy to raise the temperature of 1 kilogram of body mass by 1 degree Celsius. For the 68 kg woman in the exercise, raising her body temperature by 1 °C requires a significant amount of energy, specifically 68 kg multiplied by 3500 J/kg·K.
This property is critical in understanding how our bodies regulate temperature and cope with different environmental conditions. Calculating the specific heat helps determine the total energy required for temperature changes.

Shivering and Body Temperature

Shivering is the body's natural response to cold. It generates heat through muscle contractions, helping to restore and maintain normal body temperature. When exposed to cold, the body increases its metabolism, which can produce heat to counteract the cold environment.
As mentioned in the original problem, shivering produces about 290 watts of heat per square meter of body surface area. The woman in the exercise, with a body surface area of 1.8 m², therefore generates significant heat when she shivers. This process is particularly effective because producing heat internally means the body's core can warm up even when it's cold outside.
In simple terms, the muscle activity during shivering generates heat, and this heat helps raise the body's temperature, which in this exercise, aims at increasing her internal temperature by 1 °C.

Thermodynamics in Biology

Thermodynamics principles apply to biological systems and help explain phenomena such as how organisms maintain homeostasis. Specifically, the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed, is crucial here.
In biological systems, food intake is a source of energy, and processes like muscle contractions during shivering transform chemical energy into heat energy, a form of thermal energy. This transformation is vital for maintaining body temperature, especially in cold environments.

• Energy Conservation and Conversion: The energy from food is converted into useful work and heat.
• Heat Exchange: The body loses or gains heat depending on the environment.

This exercise showcases a real-world application of thermodynamics: how the human body uses shivering to generate heat, ensuring that body temperature remains stable despite external temperature changes.