Thermodynamics

4–22E Hydrogen is contained in a piston–cylinder deviceat 14.7 psia and 15 ft 3 . At this state, a linear spring (F ∝ x)with a spring constant of 15,000 lbf/ft is touching the pistonbut exerts no force on it. The cross-sectional area of the pistonis 3 ft 2 . Heat is transferred to the hydrogen, causing it toexpand until its volume doubles. Determine (a) the final pressure,(b) the total work done by the hydrogen, and (c) thefraction of this work done against the spring. Also, show theprocess on a P-V diagram.4–23 A piston–cylinder device contains 50 kg of water at250 kPa and 25°C. The cross-sectional area of the piston is0.1 m 2 . Heat is now transferred to the water, causing part of itto evaporate and expand. When the volume reaches 0.2 m 3 ,the piston reaches a linear spring whose spring constant is100 kN/m. More heat is transferred to the water until the pistonrises 20 cm more. Determine (a) the final pressure andtemperature and (b) the work done during this process. Also,show the process on a P-V diagram. Answers: (a) 450 kPa,147.9°C, (b) 44.5 kJChapter 4 | 2034–19 The equation of state of a gas is given as v(P 4–24 Reconsider Prob. 4–23. Using the EES software,10/ v 2) R u T, where the units of v and P areinvestigate the effect of the spring constant onm 3 /kmol and kPa, respectively. Now 0.5 kmol of this gas is the final pressure in the cylinder and the boundary work done.expanded in a quasi-equilibrium manner from 2 to 4 m 3 at a Let the spring constant vary from 50 kN/m to 500 kN/m. Plotconstant temperature of 300 K. Determine (a) the unit of the the final pressure and the boundary work against the springquantity 10 in the equation and (b) the work done during this constant, and discuss the results.isothermal expansion process.4–25 Determine the boundary work done by a gas during4–20 Reconsider Prob. 4–19. Using the integration an expansion process if the pressure and volume values atfeature of the EES software, calculate the work various states are measured to be 300 kPa, 1 L; 290 kPa,done, and compare your result with the “hand-calculated” 1.1 L; 270 kPa, 1.2 L; 250 kPa, 1.4 L; 220 kPa, 1.7 L; andresult obtained in Prob. 4–19. Plot the process described in 200 kPa, 2 L.the problem on a P-v diagram.4–26 A piston–cylinder device initially contains 0.25 kg4–21 Carbon dioxide contained in a piston–cylinder device of nitrogen gas at 130 kPa and 120°C. The nitrogen isis compressed from 0.3 to 0.1 m 3 . During the process, now expanded isothermally to a pressure of 100 kPa.the pressure and volume are related by P aV 2 , where a Determine the boundary work done during this process.8 kPa · m 6 . Calculate the work done on the carbon dioxide Answer: 7.65 kJduring this process. Answer: 53.3 kJA = 0.1 m 2H 2 Om = 50 kgFIGURE P4–23N 2130 kPa120°CFIGURE P4–264–27 A piston–cylinder device contains 0.15 kg of air initiallyat 2 MPa and 350°C. The air is first expanded isothermallyto 500 kPa, then compressed polytropically with apolytropic exponent of 1.2 to the initial pressure, and finallycompressed at the constant pressure to the initial state. Determinethe boundary work for each process and the net work ofthe cycle.Closed System Energy Analysis4–28 A 0.5-m 3 rigid tank contains refrigerant-134a initiallyat 160 kPa and 40 percent quality. Heat is now transferred tothe refrigerant until the pressure reaches 700 kPa. Determine(a) the mass of the refrigerant in the tank and (b) the amountof heat transferred. Also, show the process on a P-v diagramwith respect to saturation lines.4–29E A 20-ft 3 rigid tank initially contains saturated refrigerant-134avapor at 160 psia. As a result of heat transfer fromthe refrigerant, the pressure drops to 50 psia. Show theprocess on a P-v diagram with respect to saturation lines, anddetermine (a) the final temperature, (b) the amount of refrigerantthat has condensed, and (c) the heat transfer.