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Using Energy Concepts and the Ideal Gas ModelFour-tenth lb
Chapter 3, Problem 119P(choose chapter or problem)
Four-tenth lb of air, initially at \(540^{\circ} \mathrm{R}\), is contained in a closed, rigid tank fitted with a paddle wheel that stirs the air until its temperature is \(740^{\circ} \mathrm{R}\). The driveshaft of the paddle wheel rotates for 60 seconds at 100 RPM with an applied torque of \(20 \mathrm{ft} \cdot \mathrm{lbf}\). Assuming ideal gas behavior for the air, determine the work and heat transfer, each in Btu. There are no overall changes in kinetic or potential energy.
Questions & Answers
QUESTION:
Four-tenth lb of air, initially at \(540^{\circ} \mathrm{R}\), is contained in a closed, rigid tank fitted with a paddle wheel that stirs the air until its temperature is \(740^{\circ} \mathrm{R}\). The driveshaft of the paddle wheel rotates for 60 seconds at 100 RPM with an applied torque of \(20 \mathrm{ft} \cdot \mathrm{lbf}\). Assuming ideal gas behavior for the air, determine the work and heat transfer, each in Btu. There are no overall changes in kinetic or potential energy.
ANSWER:Step 1 of 3:
Consider an ideal gas is kept inside a rigid tank fitted with a paddle. The drive shaft rotates for 60 seconds and the temperature is increased. The torque applied is given and we are going to find the work and the heat transfer by assuming no change in potential and kinetic energy.
The mass of air m = 4/10 lb = 0.4 lb
The initial temperature T1 = 540°R
The final temperature T2 = 740°R
The time of operation Δt = 60 s
The angular speed ⍵ = 100 rpm = 10.47 rad/s
The torque 𝜏 = ft · lbf