Is hobby relay adequate for air conditioner automation with microprocessor
Switching contacts don't like inductors- anything wound like a motor or transformer. The more inductance the worse it is, and an air conditioner will be very inductive. The problem is that in an inductor, current keeps flowing when you turn off the voltage (that's what inductance is, basically) as energy is stored in the magnetic field, so as switch contacts break you get arcing which rapidly ruins them unless they are adequately designed.

Short answer: no, this isn't the right relay. You should find one rated for the inductive load and if you want it to last, you should over-specify as generously as possible.