Outgoing flight with connection in China

Hi
If I arrive in Beijing and my outgoing ticket from PEK (to a third country) has a connection in another Chinese city (e.g. Shenzhen or Hangzhou), am I eligible for 72 hour transit without visa?
If I am limited to 24 hours, does my departure from PEK have to be within 24 hours, or is it the connecting flight that has to be schedule to leave within 24 hours of my arrival in PEK?
many thanks