It definitely won't increase by a factor of two; that would be a perfectly efficient increase in throughput. That's not possible since there's always some overhead. How much benefit you get will depend on a few factors:
It may not increase at all if the OS or programs you're running on it aren't equipped to schedule processes on different cores.
It might only increase by a little if the tasks you're doing aren't very parallelizable (e.g. they depend heavily on I/O or other slow non-CPU operations).
It might increase by a good deal if the tasks are "embarrassingly parallel", e.g., long runs of identical floating-point computations or prime-number factorization.
It might make things worse if there's too much context-switching because of dependencies between the processes, or if you need to sync things across the processes.