C172 INSTRUCTOR PLT DESCRIBES DEP FROM TPA ON WRONG RWY RESULTING IN ATC ISSUED ABORT TO ACR DEP FROM INTERSECTING RWY.

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I COMMENCED AN IFR XCOUNTRY TRAINING FLT WITH A RTE AS FOLLOWS: SFB-TPA-VRB-MLB-SFB. WE DEPARTED SFB AND HAD AN UNEVENTFUL FLT TO TPA. ENRTE TO TPA; WE REQUESTED A PRACTICE ILS APCH TO RWY 18L; WHICH WAS GRANTED. UPON TOUCHDOWN; WE EXITED THE RWY; CONTACTED GND AND WERE TOLD TO TAXI TO THE RAMP. WE TAXIED TO THE SE RAMP; BOUNDED BY TXWYS E AND R AT FBO. PRIOR TO CALLING FOR TAXI CLRNC; I BRIEFED THE STUDENT AS TO THE CONCERNS WITH TXWYS E AND R AND AS PER ATIS; THAT WE COULD PROBABLY EXPECT RWY 18L. AT THIS TIME; WE CALLED FOR OUR TAXI CLRNC. WE WERE TOLD TO TAXI TO RWY 9 AT TXWY E AND HOLD SHORT. UPON ARR AT THE HOLD SHORT LINE OF RWY 9; THE STUDENT CALLED GND FOR A CLRNC TO CROSS. THE STUDENT WAS TOLD TO CONTACT TWR ON 119.5. AT THIS TIME; IT BECAME APPARENT THAT THE INTENTION WAS FOR US TO DEPART FROM THIS INTXN. WHILE HOLDING IN POS; THE STUDENT PROCEEDED TO EXECUTE A LINE-UP CHKLIST. AT THIS TIME; A KING AIR TOOK OFF ON RWY 27. THE EXCHANGE FROM THIS POINT FORWARD; TO THE BEST OF MY RECOLLECTION; IS AS FOLLOWS: STUDENT: 'SKYHAWK X IS HOLDING SHORT ON TXWY E OF RWY 9.TWR:'AFTER TKOF; L HDG 060; TURN R; CLR FOR TKOF.' STUDENT: 'CLR FOR TKOF.' AS WE WERE TAXIING INTO POS; WE EXECUTED A 180 DEG TURN ON THE RWY IN PREPARATION FOR TKOF ROLL. AT NO TIME DID THE TPA TWR STATE THE NAME OF THE ASSIGNED RWY. CONCURRENTLY; TPA TWR CLRED AN ACR FOR TKOF ON RWY 18R; WHICH STRUCK ME AS STRANGE. I QUESTIONED IT IN MY HEAD; BUT THOUGHT THAT AS OUR FLT PATH AND TURN OUT WOULD HAVE US TURNING PRIOR TO REACHING RWY 18R; THAT THIS MUST BE HOW THEY DID IT AT TPA. IMMEDIATELY UPON WHEELS UP; I REALIZED THE FAULT IN MY REASONING. ALMOST SIMULTANEOUSLY; TPA CANCELED THE HVY'S CLRNC. I TOOK THE FLT CTLS AND EXECUTED A CLBING L TURN AT APPROX 200-300 FT AGL PRIOR TO XING THE DEP END OF RWY 27 AND APPROX 1500-2000 FT PRIOR TO RWY 18R. THE RADIO CALLS ARE AGAIN; AS FOLLOWS: TWR: 'ACR X; CANCEL CLRNC; TFC DEPARTING IN THE WRONG DIRECTION.' 'ACFT X I SEE YOU'VE SEEN YOUR MISTAKE.' INSTRUCTOR: 'YES SIR; WE DO; WE'RE TURNING NOW. WE'RE VERY SORRY SIR; ACFT X.' TWR 'ACFT X; CONTINUE TURN TO 060 DEGS; 1600 FT ON THE ALT AND OVER TO DEP 119.9.' INSTRUCTOR: 'L TO 060 DEGS 1600 FT ON THE ALT; OVER TO DEP 119.9; AND WE'RE VERY SORRY FOR OUR MISTAKE.' THE CONVERSATION THAT THE STUDENT AND I HAD FOCUSED ON A COUPLE OF KEY AREAS; ASSUMPTION; COM BREAKDOWN; AND ATC QUERY: 1) WE ASSUMED THAT SINCE THE PRECEDING ACFT WERE DEPARTING TO THE W; WE WERE AS WELL. 2) TPA TWR DID NOT STATE THE RWY IN THE TKOF CLRNC; NOR DID WE STATE IT ON THE READBACK. THE LOGIC ASSOCIATED WITH THE PRECEDING ACFTS' DIRECTION OF DEPS WAS SO STRONG THAT IT CAUSED US TO TURN R AS INSTRUCTED; THEN 180 DEGS ON THE RWY TO DEPART AS HAD THE PRECEDING ACFT. 3) WE BOTH FOUND THIS CLRNC STRANGE; BUT UNFORTUNATELY ELECTED NOT TO QUESTION THE TWR. THE ARPT'S PROCS WERE NOT VERY FAMILIAR TO EITHER OF US AND AS SUCH; WE THOUGHT THAT THIS WAS A STANDARD DEP FROM THIS INTXN.