Product review (5 stars): Exact replacement, fixes the problem outlined in my description.
On an 80 series Kenmore Dryer, a gas coil failure can be determined by a few observations.

1.  Dryer will operate and heat up initially, but then cool down but continue to run through its cycle.  Clothes may feel damp and cold upon examination after the dryer cycle ends.  Your dryer will not heat up again during the cycle, and requires a lengthy cool down before heating up again. (if your dryer fails to heat up at all, this coil is not likely to be the culprit).

2.  Dryer will heat up for a short time, but fail to maintain heat, this can be observed by holding your hand against your dryer exhaust tube (being careful to feel for heat before making physical contact).

3.  Dryer will make an audible noise after the heat stops working,  lasting 10 seconds on average, and repeating the noise every 30 seconds or so.  The noise should be mechanical in nature, and should be present regardless of temp settings, or dryer setting  (air dry cycle is an exception, as the coil should not be operating during this cycle if your dryer has the setting).  The noise made by a faulty coil may not be present in all circumstances.

Replacing the coils requires knowledge of how to remove the front lower panel of your dryer, some dryers may not have a separate lower panel and will require the removal of the entire front panel.  Methods for removal will vary by model, but only requires screw drivers and/or nut driver hand tools.  Coils should be housed near the heat assemble, and held in place with a bracket, which may need to be removed entirely to remove the old coils.  Alignment points on the coils will guide the re-assembly, and the electrical connections are easy to figure out.

Please consult videos on-line about the process, and seek professional assistance if you are unsure about your abilities to perform this repair.