A student wants to lose some weight. He knows that rigorous...

A student wants to lose some weight. He knows that rigorous aerobic activity uses about $700 \mathrm{kcal} / \mathrm{h}$ $(2900 \mathrm{kJ} / \mathrm{h})$ and that it takes about $2000 \mathrm{kcal}$ per day $(8400 \mathrm{kJ})$ just to support necessary biological functions, including keeping the body warm. He decides to burn calories faster simply by sitting naked in a $16^{\circ} \mathrm{C}$ room and letting his body radiate calories away. His body has a surface area of about $1.7 \mathrm{m}^{2}$, and his skin temperature is $35^{\circ} \mathrm{C}$. Assuming an emissivity of $1.0,$ at what rate (in kcal/h) will this student "burn" calories?

Key Concepts

Blackbody Radiation

Blackbody radiation is the phenomenon wherein an object emits electromagnetic radiation solely as a function of its temperature. It provides a fundamental model for understanding how all objects at a given temperature radiate energy, with an idealized emitter (a blackbody) emitting the maximum possible energy at every wavelength.

Stefan-Boltzmann Law

The Stefan-Boltzmann law is a principle in thermal physics that states the power radiated per unit area of a surface is directly proportional to the fourth power of the absolute temperature of that surface. This law is essential for calculating the total energy loss through thermal radiation, as it connects an object's temperature with the energy it emits.

Emissivity

Emissivity is a dimensionless measure of an object's efficiency in emitting thermal radiation, relative to that of an ideal blackbody. An emissivity value of 1 indicates a perfect emitter, while values less than 1 represent surfaces that emit less radiation. This factor is crucial when applying the Stefan-Boltzmann law to real-world objects.

Radiative Heat Transfer

Radiative heat transfer is the process of energy loss or gain by radiation. It involves the exchange of energy through electromagnetic waves and is influenced by factors such as temperature, surface area, and emissivity. This concept is key to understanding how bodies lose heat in an environment, as it allows for the calculation of the net rate of energy flow due to thermal radiation.

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