The figure shows data for a portion of the ducting in a ventilation system operating at steady state. The ducts are well insulated and the pressure is very nearly 1 atm throughout. The volumetric flow rate entering at state 2 is $AV_2 = 2800 ft^3/min$. Assume the ideal gas model for air with $c_p = 0.24 Btu/lb \cdot ^\circ R$ and ignore kinetic and potential energy effects.
Determine the temperature of the air at the exit, in $^\circ F$, and the rate of entropy production within the ducts, in $Btu/min \cdot ^\circ R$.
Step 1
Determine the temperature of the air at the exit, in $^\circ F$, and the rate of entropy production within the ducts, in $Btu/min \cdot ^\circ R$.
Step 2
Determine the rate of entropy production within the ducts, in $Btu/min \cdot ^\circ R$.
$\dot{\sigma}_v = $ [ ] $Btu/min \cdot ^\circ R$
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(AV)$_1 = 5000 ft^3/min$
$T_1 = 80^\circ F$
$c_p = 0.24 Btu/lb \cdot ^\circ R$
$p = 1 atm$
(AV)$_2$
$T_2 = 40^\circ F$
$ft^3/min$
Insulation
3
$V_3 = 400 ft/min$
$T_3 = ?$