If air at sea level with a temperature of 27degrees C is forced up a mountain slope and the air's dew point at the condensation level is 14degrees C, at what elevation will condensation begin?

Answer 1

The decrease in temperature with rising altitude is 6.49 °C/1,000 m, according to ICAO definition, see:
http://en.wikipedia.org/wiki/Lapse_rate

Thus, to reach the dew point, the air mass must decrease (27-14)=13 degrees C, which translates to a rise in altitude of
(13 degrees C)/(6.49 degrees C / 1000 m)
= 2003 m
= 2000 m approximately
assuming no loss or gain in humidity of the air mass.