Beijing airport to city sight seeing and back

Yes, you can go to the downtown for a short visit. To leave the airport, you have to apply for a stay permit at the inspection counter first.

During the 10h stopover, you can visit the Tiananmen Square, outside Forbidden City and Qianmen. For the 14h on back way, I suggest you go to Temple of Heaven for a visit and then head for Wangfujing Pedestrian Street for shopping and dining.

By the way, you can make full use of the time to fulfill a good trip and then take a taxi back to PEK to catch your flight! Have fun!