Unless they're retrofitted, most older homes do not have high efficiency insulation. Because of this, the system as a whole is not balanced. In this case, an HVAC system works harder to heat or cool the home year-round and closing off rooms will limit the running time of the HVAC system, making it cheaper to run. This is especially true if the closed-off room has no cold air return ducts.
Modern homes are fully insulated with less air leakage and a higher thermal gain, meaning they retain heat or cold every time the HVAC system runs. Modern HVAC systems are balanced between rooms, and if a room is closed off, that imbalance may cause the system to function poorly. In extreme cases, it could cause a total system failure.
Unless the air ducts are in a space that is serviced by the HVAC system, they will leak when a room or a vent is closed off. Leaking ducts cause heated or cooled air to be wasted, and the pressure buildup inside closed ductwork may have adverse effects on your HVAC system. The farther a duct or room is from the forced air fan, the less effect it will have on the balance of an HVAC system if it is closed off.
In all modern insulated homes serviced by an HVAC system, it is less expensive to heat or cool rooms if they -- or their supplying ductwork -- stays open. In older homes or homes with alternative heating sources, it is cheaper to turn the HVAC system off completely and heat with the alternative source. When cooling, it is cheaper to run fans and turn off the entire HVAC system.
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