a hot water urn was turned on before shabbos but before it had a chance to boil there was a blackout in the area and there was no electricity. About a half hour into shabbos, the electricity turned back on and the urn did also. The water in the urn boiled soon afterwards. Is one permitted to use the hot water from the urn on shabbos?

Shalom, Using power after it re-ignites on Shabbat is an interesting question. Without getting into all the details, if a Jew broke Shabbat by repairing the electricity, there are serious questions about benifiting from it on Shabbat. However, in most cases, serious health or security risks allow the repair of an outage. Outside Israel, where the electricity is repaired by and for the majority of non-Jewish residents, there are good grounds to allow benefiting from the power when it comes back on during Shabbat. Assuming that your situation was one which allowed benefit from the electrical repair, we can turn to your question. Although there is a debate about the halacha, in the Hebrew section of this site, Rabbi Zalman Melamed, the Rosh Yeshiva of Bet El addressed a similar situation (http://www.yeshiva.org.il/midrash/shiur.asp?id=3764). There he rules that the water may be used after it heats up on Shabbat. This is because the water was placed in the urn before Shabbat, and one did no action to heat it up on Shabbat, as the power came back on without your intervention. This is especially the case with water, as there is no halachic problem of being tempted to stir the water to speed up its cooking, as plain water naturally circulates without needing to be stirred. May your Shabbatot be full of light, Blessings