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Step1/2

The net heat flow to or from a person depends on various factors such as the ambient temperature, wind speed, humidity, the person's clothing, and activity level. Assuming that the person is at rest and wearing typical clothing, we can estimate the net heat flow based on the given conditions: a. Indoors, in an environment at 20°C: In this case, the net heat flow will be negligible as the person's body temperature is close to the ambient temperature, and there is no significant temperature difference to drive heat transfer.

b. Outdoors on a clear night, with a ground air temperature of 15°C (assume atmospheric temperature of -20°C): In this scenario, the person's body heat will flow to the colder surroundings since the ambient temperature is lower than their body temperature. The net heat loss will depend on the temperature difference, wind speed, and humidity. Assuming a wind speed of 0 m/s and low humidity, we can estimate the net heat loss using the following formula: Q = \( \mathrm{{h}{A}{\left({T}_{{{b}{o}{\left.{d}{y}\right.}}}-{T}_{{{s}{u}{r}{r}{o}{u}{n}{d}{i}{n}{g}{s}}}\right)}} \)

Explanation

where Q is the net heat transfer rate in watts, h is the convective heat transfer coefficient, A is the person's surface area in \( \mathrm{{m}^{{2}}} \), \( \mathrm{{T}_{{{b}{o}{\left.{d}{y}\right.}}}} \) is the person's body temperature (assumed to be 37°C), and \( \mathrm{{T}_{{{s}{u}{r}{r}{o}{u}{n}{d}{i}{n}{g}{s}}}} \) is the ambient temperature (15°C).

The convective heat transfer coefficient for a stationary person in still air is typically around 10 W/(m^2*K).

Using these values, we get: \( \mathrm{{Q}={10}\times{1.8}\times{\left({37}-{15}\right)}={396}{W}} \) This means that the person will lose about 396 watts of heat to the surroundings, which will cause their body temperature to drop over time.

Explanation: Please refer to solution in this step.

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c. Outdoors on a clear day, at 25°C air temperature, in direct sunlight: In this case, the person's body will absorb heat from the surroundings, mainly through radiation from the sun. The net heat gain will depend on the person's orientation to the sun, their clothing, and their body's ability to dissipate heat. Assuming that the person is facing the sun and wearing typical clothing, we can estimate the net heat gain using the following formula: \( \mathrm{{Q}={A}\timesα\times{\left({1}-ρ\right)}\times{I}} \) where Q is the net heat transfer rate in watts, A is the person's surface area in \( \mathrm{{m}^{{2}}} \), α is the person's absorptivity (assumed to be 0.7), ρ is the person's reflectivity (assumed to be 0.3), and I is the solar irradiance in watts per square meter (assumed to be \( \mathrm{{1{,}000}\frac{{W}}{{m}^{{2}}}} \)). Using these values, we get: \( \mathrm{{Q}={1.8}\times{0.7}\times{\left({1}-{0.3}\right)}\times{1{,}000}={756}{W}} \)

This means that the person will absorb about 756 watts of heat from the surroundings, which will cause their body temperature to rise over time. Note that this calculation assumes that the person's body is in thermal equilibrium with the surroundings, which may not be the case if the person's body is actively dissipating heat through sweating or other mechanisms.

Explanation: Please refer to solution in this step.

What would the net heat flow to/from a person be if they were: a. indoors, in an environment at 20 °C? b. outdoors on a clear night, with a ground air temperature of 15 °C (assume atmospheric temperature of -20 °C)? c. outdoors on a clear day, at 25 °C air temperature, in direct sunlight?

Public Answer

What would the net heat flow to/from a person be if they were:
a. indoors, in an environment at 20 °C?
b. outdoors on a clear night, with a ground air temperature of 15 °C (assume atmospheric
temperature of -20 °C)?
c. outdoors on a clear day, at 25 °C air temperature, in direct sunlight?