Romulan plasma torpedo from "Balance of terror"
Enterprise firepower from "Taste of armageddon"The plasma torpedo, seen in "Balance of Power," disintegrated quite thoroughly the fourth UFP outpost it attacked; this outpost was "a mile deep on an asteroid. Almost solid iron." With the first shot, the Romulan ship took out the deflectors and damaged the station severely; the second shot then disintegrated the asteroid and outpost into "dust and debris" - by "forcing an implosion." To crush a two mile diameter asteroid mostly comprised of iron into dust using glowing hot plasma requires a great deal of work. Considering the presence of some debris, the yield could be guessed at being perhaps only a hundred gigatons or so - a truly impressive sum, particularly for a ship as small as the Romulans'. It is not surprising in the least that the ship appears to have the capability to fire only 5-10 (probably 9) shots before needing to refuel.
Firepower from "Whom Gods destroy"In "A Taste for Armageddon," Kirk states bluntly: "In two hours, the Enterprise will destroy Eminiar 7." In this particular context, it appears as though the Enterprise has quite enough firepower to level all civilization of Eminar 7, which has been fortifying and stockpiling weapons for the past 500 years, in a fairly short span of time. Similar reference to this capability occur in "Bread and Circuses" and "Operation: Annihilate!" Kirk agonizes over obliterating a human colony with a million people in order to destroy the neural parasites that have infested it in the latter, while in the former, an ex-captain, worried, notes that the Enterprise would be able to wipe out the 20th century version of a planetary Roman Empire.
Incidentally, we could use this to check our yield estimates. We may estimate that destroying Eminar 7 involves levelling reinforced concrete buildings over perhaps a total of 1-25% of the planet's surface; with efficient thermal weaponry, this may be somewhere around ~20kt per square kilometer. With a surface area for an Earthlike planet of about a half billion, this gives us - very generally - 100 gigatons to perhaps 2.5 teratons or so that the U.S.S. Enterprise is expected to deliver in short order. This is generally agreeable with our rough estimates of phaser and photon torpedo yields from various episodes.
"The Paradise Syndrome" shows Spock trying to split into pieces an asteroid stated to be nearly the size of Earth's moon using phasers after failing to deflect it sufficiently using the ship's deflector screens. Even considering that he was attempting to take advantage of a "weak spot" in the asteroid, as well as the asteroid being somewhat less than actually moon-sized, this would require zettajoules of imparted energy if not yottajoules to pull off - i.e., the equivalent of gigatons to teratons of TNT. The actual effect achieved is somewhat less impressive; the first normal phaser blast used on the asteroid produces a splash of glow about a third the diameter of the asteroid; a full broadside with the phasers only causes a small square of the asteroid to glow molten red.
++http://www.starfleetjedi.net/Square_Blast.jpg
If the asteroid's longer dimension is a bit over 1700 km, then the area melted is about 70 km across and roughly square. The heat of fusion for lava is generally similar to the energy required to heat the rock ~300 kelvins; granite generally melts at about 925 kelvins; if we approximate it as being granite chemically and having a bulk density of 2 tons per cubic meter, melting a 70 km cube out of the asteroid gives only ~130-160 exajoules for a full power broadside by the Enterprise. With four phasers being fired on full power here, that's a maximum strength blast of 30-40 EJ per phaser - 7-10 gigatons. Considering that it may not have truly been an entire 70 km cube melted, but likely a smaller fraction, we should call it perhaps 1-10 gigatons for a ship's phaser on full blast.