A piston–cylinder device initially contains 1.2 kg of air at 700 kPa and 200°C. At this state, the piston is touching on a pair of stops. The mass of the piston is such that 600-kPa pressure is required to move it. A valve at the bottom of the tank is opened, and air is withdrawn from the cylinder. The valve is closed when the volume of the cylinder decreases to 80 percent of the initial volume. If it is estimated that 40 kJ of heat is lost from the cylinder, determine (a) the final temperature of the air in the cylinder, (b) the amount of mass that has escaped from the cylinder, and (c) the work done. Use constant specific heats at the average temperature.
FIGURE P5–183
(a)
The final temperature of air in the cylinder.
Answer to Problem 183RP
The final temperature of air in the cylinder is
Explanation of Solution
Write the equation of mass balance.
Here, the inlet mass is
The change in mass of the system for the control volume is expressed as,
Here, the suffixes 1 and 2 indicates the initial and final states of the system.
Consider the piston-cylinder as the control volume. Initially the cylinder is filled with air and the valve is in closed position, further no other mass is allowed to enter the cylinder. Hence, the inlet mass is neglected i.e.
Rewrite the Equation (I) as follows.
Write the formula for initial volume of air present in the cylinder.
Here, the mass of air is
Write the formula for mass of air present in the cylinder at final state.
Here, the subscript 2 indicates the final state.
Write the energy balance equation.
Here, the heat transfer is
The pressure of
The Equation (V) reduced as follows.
Write the formula for boundary work done on the cylinder.
Here, the pressure required to move the piston is
The enthalpy and internal energy in terms of temperature and specific heats are expressed as follows.
Rewrite the Equation (VI) as follows.
The temperature of the air while exiting the cylinder is considered as the average temperature of initial and final temperatures.
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2b, “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
Conclusion:
Substitute
It is given that the final volume is 80 % of initial volume.
Substitute
Substitute
Substitute
Substitute
Use Engineering Equation Solver (EES) or online calculator to solve the Equation (X) and obtain the value of
Thus, the final temperature of air in the cylinder is
(b)
The amount of mass escaped from the cylinder.
Answer to Problem 183RP
The amount of mass escaped from the cylinder is
Explanation of Solution
The amount of mass escaped from the cylinder is nothing but the mass of air vented out until final state i.e.
Refer Equation (II) and (IX).
Conclusion:
Substitute
Thus, the amount of mass escaped from the cylinder is
(c)
The work done.
Answer to Problem 183RP
The amount of mass escaped from the cylinder is
Explanation of Solution
The work done is nothing but the work done on the piston to move it i.e. boundary work
Refer part (a).
Thus, the work done is
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Chapter 5 Solutions
Thermodynamics: An Engineering Approach
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