Question

Please solve all parts, showing work. Included is an equation sheet for reference.

Some numbers you should get (please still solve all parts) are b) 81.2 mol c) 1.013 Mpa d) 1554 K e) Wcyc= 1595 J f) deltaEint12= 4559 J g) Q31= -2964 J i) deltaS13= 3.888 J/K

Thank you in advance!

1) (60 points) A heat engine uses air (diatomic as the working muid in a three-step cycle. First, a volume of 2 L (2 x 10-3 m3) at 300 K and 1 atm (state 1) is heated under constant volume to a temperature of 3000 K (state 2). Second, the gas is expanded adiabatically to a pressure of 1 atm (state 3) and volume 10.36 L (10.36 x 10-3 m3). Third, the gas is allowed to cool under constant pressure back to the original state (state 1). (a) the three-step cycle on a P-v diagram and name each leg in the process. Label states 1. 2, and 3. (b) Calculate the number of moles of the gas. (c) Calculate the pressure at state 2. (d) Calculate the temperature at state 3. (e) Calculate the work done by the gas during each of the process steps 1-2, 2-3, and 3-1 and for the entire cycle. (f Calculate the change in internal energy of the gas during each of the process steps 1.2, 2-3, and 3-1 and for the entire cycle. (go Calculate the heat added to the gas during each of the process steps 1-2, 2-3, and 3-1 and for the entire cycle. (h) Using the previous heat and work calculations for the cycle, draw the schematic heat engine diagram and assign all the numbers. Calculate the heat engine efficiency over the cycle. (i) Calculate the change in entropy during each of the process steps 1-2, 2-3, and 3-1 and for the entire cycle. Does the engine obey the second la Explain.

Answer 1

a) b) PV = n R T n = 1.01 times 10^5 times 2 times 10^- 3/8.314 times 300 n = 0.08124 moles. C) P_ 1/T_ 1 = P_ 2/T_ 2 rightdoublearrow P_ 2 = 10 atm = 1.03 times 10^6 pa = 1.013 Mpa d) T = P_ 3V_ 3/n R = 1554 k.