A new high-efficiency home heating system includes an air-to-air heat exchanger that uses energy from outgoing stale air to heat the fresh incoming air. If the outside ambient temperature is −10◦C and the relative humidity is 50%, how much water will have to be added to the incoming air if it flows in at the rate of 1 m3/s and must eventually be conditioned to 20◦C and 45% relative humidity?