graduate admissions - How do I politely ask a professor to contact another professor he knows to accept me as PhD student?

I sent an email to a professor for possible acceptance as a PhD student, but sometimes it takes too long to hear back.

I know another professor, that has a good knowledge (experience) with the first professor. Can I ask this second professor, in polite way, to contact the first one, and discuss with him whether to accept me as a student?

Is this possible? What should I say to the second professor?