Small Group Activity: Grey space capsule
In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.
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blackbody Stefan-Boltzmann Law
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This activity follows Using the Stefan-Boltzmann law
A grey space capsule is sent on a trip to the Moon. The surface is designed to reflect 50% of the incident sunlight (i.e. it is “grey” for wavelengths less than about 3 or 4 \(\mu\text{m}\)). The total intensity of radiation emitted by the surface (wavelengths longer than about 3 or 4 \(\mu\text{m}\)) are still described by \(\sigma T^4\).
The capsule is spherical and has a radius of 3 meters.
The space capsule reaches thermal equilibrium after being bathed in sunlight for a few hours. The capsule is rotating and is made of thermally conducting metal, so that all sides have the same temperature. Find the temperature.
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