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Solved: Using Energy Concepts and the Ideal Gas ModelAs
Chapter 3, Problem 117P(choose chapter or problem)
As shown in Fig. P3.117, a fan drawing electricity at a rate of \(1.5 \mathrm{~kW}\) is located within a rigid enclosure, measuring \(3 \mathrm{~m} \times 4 \mathrm{~m} \times 5 \mathrm{~m}\). The enclosure is filled with air, initially at \(27^{\circ} \mathrm{C}, 0.1 \mathrm{MPa}\). The fan operates steadily for 30 minutes. Assuming the ideal gas model, determine for the air (a) the mass, in kg, (b) the final temperature, in \({ }^{\circ} \mathrm{C}\), and (c) the final pressure, in MPa. There is no heat transfer between the enclosure and the surroundings. Ignore the volume occupied by the fan itself and assume there is no overall change in internal energy for the fan.
Questions & Answers
QUESTION:
As shown in Fig. P3.117, a fan drawing electricity at a rate of \(1.5 \mathrm{~kW}\) is located within a rigid enclosure, measuring \(3 \mathrm{~m} \times 4 \mathrm{~m} \times 5 \mathrm{~m}\). The enclosure is filled with air, initially at \(27^{\circ} \mathrm{C}, 0.1 \mathrm{MPa}\). The fan operates steadily for 30 minutes. Assuming the ideal gas model, determine for the air (a) the mass, in kg, (b) the final temperature, in \({ }^{\circ} \mathrm{C}\), and (c) the final pressure, in MPa. There is no heat transfer between the enclosure and the surroundings. Ignore the volume occupied by the fan itself and assume there is no overall change in internal energy for the fan.
ANSWER:
Part (a)
Step 1 of 6:
Consider air is enclosed in a rigid enclosure of volume V and a fan fitted with it draws power from the enclosure. Assume that air is ideal and the potential, kinetic and the effects of fan are negligible. The heat transfer between the enclosure and the environment is also zero. We are going to find the mass of air.
The power rate = -1.5 kW = -1.5 kJ/s
The volume of the enclosure V = 3 m × 4 m × 5 m = 60 m3
The initial temperature T1 = 27°C = 300 K
The initial pressure P1 = 0.1 MPa = 1 bar
The time of operation of the fan Δt = 30 min = 1800 s