A disposable paper cup is used for a couple of minutes.
But it will never be recycled.
The typical disposable paper cup is a composite. The high quality, virgin paper is coated in a thin layer of plastic. It is extremely undesirable to the recycled paper plants since they are not equipped to separate the material. In the U.S., 23 billion paper cups are landfilled per year. That is 60 million pounds of waste, 99% of which is quality paper fibers.  
23 billion paper cups in 2013 according to data from www.PaperCalculator.org and the Environmental Defense Fund. 60 million pounds of waste is based on 12 grams per cup, 0.1 gram of PE coating.
It's confusing! to recycle or to trash?
Cups were collected from Milstein Hall & the Green Dragon Cafe. Paper cups were picked out of the recycling and garbage cans in roughly similar quantities. An additional informal study showed 76% of people do not know a paper cup cannot be recycled.
DISPOSABLE & REUSABLE CUP ENERGY COMPARISON
The energy break-even point is the number of uses necessary to reach equal energy efficiency with a disposable cup. Glass, plastic, and ceramic are shown in relation to a paper cup, which would be thrown away after each use. A glass cup is comparable in energy consumption after 15 uses, for plastic 17 uses, and for ceramic 39 uses. 
Hocking, Martin B. “Reusable and Disposable Cups: An Energy-Based Evaluation.” Environmental Management 18(6), 1994, pp. 889-899.
CUP  /  PAPER PULP & PLASTIC COATING FROM CUP  /  PAPER PULP FROM VARIOUS BRANDS
Manufacture and Intervention process
MATERIAL TESTING
MODEL OF GIMME! COFFEE, N CAYUGA ST LOCATION
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