I really don't think sperm would live for 2 hours in a cup. :>)
Sperm only survives at body temperature - I'm not sure for how long.
I don't believe specialmom realized that you are a male, but she is mostly correct. If you ejaculated into a sterile cup and capped it, yet left it in the open environment, the sperm would be viable for up to 1-2 hours. The sperm viability is also dependent on factors such as temperature, and the male that they came from. If you left the specimen out any longer, the sperm would die due to exposure to the elements.
Sperm samples collected into a sterile container may remain alive for many hours, but their fertilizing capability drops dramatically after 60 minutes. Sperm exposed to room air on clothing, bed linens or toilet seats lose motility (the ability to swim) rapidly. Once the semen dries out, the sperm are usually dead.
Here's some other helpful information:
Sperm can live from several minutes to several days depending on their environment:
• Exposed to air, on a cold surface or clothing, for example, sperm usually die within minutes.
•In a closed and clean container at body temperature, sperm can survive for 4-6 hours or even more.
•Sperm can be frozen at extremely low temperatures (but not in the refrigerator) and survive for years.
•Sperm can survive in the vagina for up to several hours.
•Most sperm die in the cervix within 24-48 hours, but some can survive for 4-5 days.
•Some sperm can also survive in the fallopian tubes for several days.
It will die right away under the circumstances you detail here. Sperm samples at sperm banks are kept under special conditions and they have special equipment. Not just a cup. This can not impregnate you or someone else. good luck