Air enters the duct of an air-conditioning system at 15 psia and 50°F at a volume flow rate of 450?ft3/min. The diameter of the duct is 10 in, and heat is transferred to the air in the duct from the surroundings at a rate of 2 Btu/s. Determine (a) the velocity of the air at the duct inlet and (b) the temperature of the air at the exit.

What will be an ideal response?

Air gains heat as it flows through the duct of an air-conditioning system. The velocity of the air at the duct inlet and the temperature of the air at the exit are to be determined.

Assumptions 1 Air is an ideal gas since it is at a high temperature and low pressure relative to its critical point values of -222°F and 548 psia. 2 The kinetic and potential energy changes are negligible, ?ke ? ?pe ? 0. 3 Constant specific heats at room temperature can be used for air. This assumption results in negligible error in heating and air-conditioning applications.

Properties The gas constant of air is R = 0.3704 psia•ft3/lbm•R (Table A-1E). Also, cp = 0.240 Btu/lbm•R for air at room temperature (Table A-15E).

Analysis We take the air-conditioning duct as the system. This is a control volume since mass crosses the system boundary during the process. We observe that this is a steady-flow process since there is no change with time at any point and thus , there is only one inlet and one exit and thus , and heat is lost from the system. The energy balance for this steady-flow system can be expressed in the rate form as

(a) The inlet velocity of air through the duct is determined from

(b) The mass flow rate of air becomes

Then the exit temperature of air is determined to be