It goes without saying that the chicken is spherical for the purposes of radiation. But you don’t need to make any assumptions about its internal structure; a chicken in a vacuum is a black box, thermally speaking. Well, a black sphere.
If you’re going to heat the ambient environment, why not go all the way and perform the experiment inside an oven?
Restructuring the chicken would actually be a great idea. Its natural structure allows heat to dissipate too easily through unslapped extremities. Also, we can safely assume that this is a grocery store chicken with a central internal void where its organs used to be. That means the unslapped side of the chicken is effectively insulated from the slappable area. The chicken should at least be deboned.
Grandma was a Quaker farmwife. Grandpa raised poultry on their small suburban farm. We family ate chicken dinner with them every Sunday. Not once did I see Grandma or Grandpa slap a chicken. Maybe it’s a cultural thing.
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