A fan that consumes 20 W of electric power when operating is claimed to discharge air from a ventilated room at a rate of 1.0 kg/s at a discharge velocity of 8 m/s. Is the claim reasonable? What if the electric power is 40 W?

No, the claim is not reasonable for 20 W electric power consumption.

It is reasonable for 40 W electric power consumption.

Explanation:

Power = (1/2) * mass flow rate * (square of velocity)

mass flow rate = 1 kg/s

velocity = 8 m/s

square of velocity = 64 m^2 / s^2

Power = (1/2) * (1) * (64)

Power = 32 W

For a fan that consumes 20 W power it is not possible to deliver more power than 20 W but this one is delivering 32 W hence it is a false claim.

For a fan that consumes 40 W it is indeed possible to deliver 32 W considering the efficiency. Hence this claim is reasonable.