Can a 100 breaker box handle a 15 kw furnace?

The equation for amperage is I = W/E, Amps = Watts/Volts. The amperage for the furnace would be, Amps = 15000/240 = 62.5 amps. So to answer the question, yes a 100 amp breaker with a #4 copper conductor will be sufficient to operate a 15 kW furnace. A 70 amp breaker will work but it is cutting the edge a bit too fine as you don't need the furnace to trip off during the winter months (northern hemisphere) if you are away from your home for an extended period of time.