In a cold environment, a person can lose heat by conduction and radiation at a rate of about 200 W. Estimate how long it would take for the body temperature to drop from 36.6°C to 35.6°C if metabolism were nearly to stop. Assume a mass of 65 kg. (See Table 19–1.)

Verified step by step guidance

1. Determine the total heat loss required for the body temperature to drop from 36.6°C to 35.6°C. Use the formula for heat transfer: $Q=mc\mathrm{\Delta T}$, where $m$ is the mass of the body (65 kg), $c$ is the specific heat capacity of the human body (approximately 3480 J/(kg·°C) from Table 19–1), and $\mathrm{\Delta T}$ is the temperature change (36.6°C - 35.6°C).
2. Substitute the given values into the formula: $Q=\; (65\; \backslash ,\; \backslash text\{kg\})(3480\; \backslash ,\; \backslash text\{J/(kg·°C)\})(36.6\; \backslash ,\; \backslash text\{°C\}\; -\; 35.6\; \backslash ,\; \backslash text\{°C\})$. Simplify the expression to find the total heat loss $Q$.
3. Recognize that the rate of heat loss is given as 200 W (watts), which is equivalent to 200 J/s. Use the relationship between power, energy, and time: $P=Q/t$, where $P$ is the power, $Q$ is the total heat loss, and $t$ is the time.
4. Rearrange the formula to solve for time: $t=Q/P$. Substitute the calculated value of $Q$ from Step 2 and the given power $P=\; 200\; \backslash ,\; \backslash text\{W\}$.
5. Simplify the expression to find the time $t$, which represents how long it would take for the body temperature to drop from 36.6°C to 35.6°C under the given conditions.

Key Concepts

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object or substance to another. In this context, it occurs through conduction, where heat is transferred through direct contact, and radiation, where heat is emitted as infrared radiation. Understanding these mechanisms is crucial for estimating how quickly a person loses heat in a cold environment.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. For the human body, this value is important for calculating how much energy is needed to lower the body temperature from 36.6°C to 35.6°C. Knowing the specific heat capacity allows us to determine the total heat loss required for this temperature change.

Metabolic Rate

Metabolic rate refers to the rate at which the body converts food into energy, which is essential for maintaining body temperature. In this scenario, it is assumed that metabolism nearly stops, meaning the body is not generating significant internal heat. This assumption simplifies the calculation of how long it will take for the body temperature to drop under the influence of external heat loss.