why does the temperature of boiling water remain the same as long as the boiling continues?

Question

Because it is a pure compound undergoing a phase change. The constant temperature is a requirement of the Gibbs Phase Rule. It is not obvious why this happens. If the compound is not pure, the tempertaure will rise as it boils off the most volatile components.

Heat is required to change the liquid water to steam (from liquid to gas). As long as there is water in the boiling pot, that process will continue; i.e., water will continue to boil and change from liquid to gas. AFTER all the water has been changed from liquid to gas, THEN (and only then) will the temperature of the steam begin to rise if additional heat is added.

Answer 1

It takes allot of energy to vaporize water. Several BTUs for each change of state because it's changing the molecular structure. Not as much energy required to change temperature in same state.