When a/c compressors begin to fail they bind and usually cause the vehicles engine to stall or loose power. When the compressor locks up it will smoke the belt. Being you just replaced the a/c belt, it is grabbing better. You might try to get the a/c system serviced. Sometimes with new R134a oil and removing contaminates when the system is evacuated ,the compressors life is extended. But in my years of experience that is rare.
Good luck Mike
You are welcome. I hope you get it done at a reasonable price.