Re-using a paper from one class for another? Last year, I wrote a 10 page term paper for a geology class that focused on the geochemistry of certain rock deposits.  I received an A on the paper.  This year, I'm taking a geochemistry class at a different university and have to write another thesis paper.  This assignment has the same criterion as the other paper did and the topic I wrote on before is on of the allowed topics.

Would it be acceptable (morally and/or academically) to submit a slightly edited version of the first paper I wrote in the new class?  

The paper was not published/distributed in any way (to my knowledge), and is entirely my own work with proper citations.
Almost invariably, the answer to "Is it OK to submit X for a class assignment?" is "Ask the instructor.".

You do need to ask yourself whether your objective for the geochemistry class is to get a good grade, or to improve your knowledge and skills in the area of geochemistry, or both. Even if the instructor agrees with recycling the old paper, you may get more out of the class if you pick a different topic and write a new paper.