Solution Found!
Applying the Entropy Balance: Control VolumesFigure P6.111
Chapter 6, Problem 111P(choose chapter or problem)
Figure P6.111 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. Assuming the ideal gas model for air with \(c_{p}=0.24 \mathrm{\ Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), and ignoring kinetic and potential energy effects, determine (a) the temperature of the air at the exit, in \({ }^{\circ} \mathrm{F}\), (b) the exit diameter, in ft, and (c) the rate of entropy production within the duct, in \(\mathrm{Btu} / \mathrm{min} \cdot{ }^{\circ} \mathrm{R}\).
Questions & Answers
QUESTION:
Figure P6.111 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. Assuming the ideal gas model for air with \(c_{p}=0.24 \mathrm{\ Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), and ignoring kinetic and potential energy effects, determine (a) the temperature of the air at the exit, in \({ }^{\circ} \mathrm{F}\), (b) the exit diameter, in ft, and (c) the rate of entropy production within the duct, in \(\mathrm{Btu} / \mathrm{min} \cdot{ }^{\circ} \mathrm{R}\).
ANSWER:a.)
Step 1 of 5
We have to determine the temperature of the air at the exit.
The temperature of the air at the exit can be found by using steady state and energy balance equations.
and
For the control volume, = 0 and
= 0 and the kinetic and potential energy effects can be ignored.
Using
The above equation can be rewritten as
. . . . . . . (i)
