Problem 71 - College Physics

Question

Shivering. You have no doubt noticed that you usually shiver when you get out of the shower. Shivering is the body's way of generating heat to restore its internal temperature to the normal \(37^{\circ} \mathrm{C},\) and it produces approximately 290 \(\mathrm{W}\) of heat power per square meter of body area. \(\mathrm{A} 68 \mathrm{kg}(150 \mathrm{lb}), 1.78 \mathrm{m}\) (5 foot, 10 inch) person has approximately 1.8 \(\mathrm{m}^{2}\) of surface area. How long would this person have to shiver to raise his or her body temperature by \(1.0 \mathrm{C}^{\circ},\) assuming that none of this heat is lost by the body? The specific heat capacity of the body is about 3500 \(\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})\) .

Step-by-Step Solution

Answer

Shivering for approximately 456 seconds (or about 7.6 minutes) will raise the body temperature by 1°C if no heat is lost.

Step 1: Concept Understanding

The problem requires us to find out how long it takes for shivering to increase the body temperature by 1.0°C. Shivering generates heat, and we need to calculate the total heat required to achieve the temperature increase and then find the time to generate this heat.

Step 2: Calculate Total Heat Required

The formula to compute heat (Q) required is: \[Q = m \times c \times \Delta T\] where \(m\) is the mass of the person (68 kg), \(c\) is the specific heat capacity (3500 J/kg·K), and \(\Delta T\) is the change in temperature (1.0°C = 1.0 K). This gives:\[Q = 68 \times 3500 \times 1 = 238,000 \; \text{J}\].

Step 3: Calculate Heat Power Generated by Shivering

The total power generated by shivering is given by: \[P = 290 \; \text{W/m}^2 \times 1.8 \; \text{m}^2 = 522 \; \text{W}\]. This represents the rate at which heat is generated per second.

Step 4: Calculate Time Required to Generate the Heat

Using the formula: \[Q = P \times t\] where \(Q\) is the total heat required (238,000 J) and \(P\) is the power (522 W). Solving for time \(t\):\[t = \frac{238,000}{522} \approx 456\; \text{seconds}\].

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat energy required to raise a unit mass of the substance by 1 degree Celsius (°C) or 1 Kelvin (K). For the human body, this value is approximately 3500 J/(kg·K). This means that for each kilogram of body mass, 3500 joules of energy are needed to increase the temperature by 1 K.
This concept is crucial in energy calculations as it helps us determine how much energy is needed to cause a temperature change in a substance, thereby playing a key role in various applications including heating and cooling processes.
In the exercise, the specific heat capacity of the body helps us estimate the total energy needed to raise the person's body temperature, which is essential in understanding how shivering contributes to warming the body.

Energy Conversion

Energy conversion involves changing one form of energy into another. In the context of the given exercise, when a person shivers, the body converts chemical energy from stored nutrients into thermal energy (heat).
This heat is generated at a rate of 290 watts per square meter of body surface area, providing the warmth necessary to raise the body temperature. The concept emphasizes the body's ability to efficiently convert energy to maintain homeostasis, or the balance of internal conditions.
Understanding this conversion is vital in thermodynamics and biological studies as it explains how living organisms adapt to external temperature changes by transforming energy within the body to counteract heat loss.

Thermodynamics

Thermodynamics is the branch of physics that studies the relationships between heat, work, and energy. It provides a framework for understanding how organisms, such as humans, maintain steady internal states despite varying external conditions.
Through thermodynamic principles, we can explain the body's heat regulation. When shivering occurs, it is a response triggered by thermoreceptors that send signals, leading to muscle contractions, thereby generating heat.
The exercise demonstrates an application of thermodynamics by illustrating how energy input through shivering translates to maintaining the body's optimal temperature of 37°C. This interplay between energy and matter is a foundational concept in physics and physiology.

Body Temperature Regulation

Body temperature regulation is a key aspect of homeostasis, where the human body works to keep its internal temperature within a narrow, optimal range. The normal body temperature is usually around 37°C.
When you step out of a warm shower into a cooler environment, your body quickly detects the temperature drop. Shivering is one way the body counteracts this cooling effect by generating additional heat through muscle activities. The muscles rapidly contract and relax, converting energy to warmth.
This mechanism ensures that vital organs function properly and the body's internal processes remain stable. Understanding this response highlights the body's remarkable ability to adapt and regulate its internal environment in response to external temperature changes.