Final answer:
While the specific maximum discharge temperature for ducts is not provided in the question, a safe estimate would be around 120 to 125 degrees Fahrenheit. For heating air, the rate of heat transfer needed can be calculated using the specific heat capacity of air and the volume and temperature change required, such as 1.675 kilowatts for 500 m³ raised by 10.0°C per minute.
Step-by-step explanation:
The maximum discharge temperature for ducts of a warm air heating system is not provided in the question, but the typical upper limit for the air coming out of a furnace is around 120 to 125 degrees Fahrenheit. The exact maximum temperature can vary based on the specifications of the heating system and the materials used in the ductwork. It is important to adhere to these specifications to prevent damage to the ducts and ensure safety.
To determine the heat transfer rate necessary to warm a certain volume of air by a specific temperature increase, we can apply the heat capacity equation. The specific heat capacity of air is approximately 1.005 kJ/kg·K (kilojoules per kilogram per Kelvin). Given that 1 cubic meter of air at 20°C has a mass of about 1.204 kg, we can calculate the required energy transfer.
For example, warming 500 m³ of air by 10.0°C would require:
- 1.005 kJ/kg·K * 1.204 kg/m³ * 500 m³ * 10.0 K = 6,030 kJ
Since power is energy per unit time, and 1 kilojoule is 0.001 kilowatts-hour, we would need:
- 6,030 kJ/min * 1 kW·h/3,600 kJ = 1.675 kW
Thus, the rate of heat transfer must be at least 1.675 kilowatts to sufficiently warm the incoming air.