MD80 CREW HAD A MALFUNCTION ENG AND CABIN AND COCKPIT SMOKE IN ZKC CLASS A AIRSPACE.

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IN LEVEL FLT AT FL310; A SUDDEN JOLT WAS EXPERIENCED. WE NOTICED THAT THE L HAND EPR; N1; AND N2 WERE SURGING WITH EGT BLANK. WITHIN 2-3 SECONDS; SMOKE FILLED THE COCKPIT. WE DONNED OUR OXYGEN MASKS; DECLARED AN EMER AND INITIATED AN EMER DSCNT. I NOTICED THAT THE L ENG WAS STILL PRODUCING THRUST. THEREFORE; I WAS RELUCTANT TO SHUT DOWN THE WORKING L ENG DUE TO MULTIPLE EMERS OCCURRING AT THAT TIME; IE; SMOKE; POSSIBLE FIRE OF AN UNKNOWN SOURCE; AND ATC COM DIFFICULTY. THE L1 FLT ATTENDANT CAME TO THE COCKPIT TO RPT THAT SMOKE HAD FILLED THE CABIN. I TOLD HER TO PREPARE FOR AN EMER LNDG. I ALSO MADE A PA ANNOUNCEMENT INFORMING THE PAX AND CREW THAT WE WOULD BE LNDG IN ABOUT 10 MINS. WE INITIALLY INTENDED TO PROCEED TOWARD MCI BUT I NOTICED THAT WE WERE ABOUT 80 MI FROM THE ARPT; SO I INFORMED THE CTLR THAT WE NEEDED VECTORS TO THE NEAREST SUITABLE ARPT. THE CTLR STATED THAT ZZZ WAS ABOUT 20 MI AWAY; SO I AGREED TO BE VECTORED TOWARDS THE BASE. WE CONTINUED TO DSND ON RADAR VECTORS; AND ABOUT 7-10 MI FROM THE ARPT WE GAINED SIGHT OF RWY 19. I ENTERED INTO AN APCH SLOT FOR LNDG AND REDUCED SPD. I WAS AWARE THAT THE LNDG WOULD BE OVERWT; THEREFORE; I SMOOTHLY LANDED THE ACFT AND APPLIED R REVERSE THRUST WITH MINIMUM BRAKING TO AVOID TIRE DAMAGE OR BRAKE OVERHEAT. ONCE STOPPED; THE BRAKES WERE SET AND I THEN CALLED FOR THE EVAC CHKLIST; AND INFORMED THE L1 FLT ATTENDANT TO INITIATE AN EVAC FROM THE R SIDE ONLY. I THEN MADE A PA ANNOUNCEMENT REINFORCING THE EVAC COMMAND AND ASKED THE PAX TO REMAIN CALM BUT QUICKLY MOVE TO THE EMER EXITS. I THEN ASSISTED WITH THE EVAC AND WAS THE LAST PERSON TO LEAVE THE ACFT THROUGH THE R OVERWING EXIT. THE CREW THEN DIRECTED THE PAX AWAY FROM THE ACFT TO A SAFE DISTANCE.