A monatomic ideal gas has pressure pi and temperature Ti. It is contained in a cylinder…
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Question “A monatomic ideal gas has pressure pi and temperature Ti. It is contained in a cylinder…”
A monatomic ideal gas has pressure pi and temperature Ti. It is contained in a cylinder of volume V1 with a movable piston, so that it can do work on the outside world. Part A Consider the following three-step transformation of the gas: 1. The gas is heated at constant volume until the pressure reaches Apı (where A>1). 2. The gas is then expanded at constant temperature until the pressure returns to Pi. 3. The gas is then cooled at constant pressure until the volume has returned to Vi. How much heat Q1 is added to the gas during step 1 of the process? Express the heat added in terms of p1, Vi, and A. View Available Hint(s) It may be helpful to sketch this process on the pV plane. EVO AED ? 0,Q_1 = Submit Part B How much work W2 is done by the gas during step 2? Express the work done in terms of p1, Vi, and A. View Available Hint(s) IVO AEO ? W W_2 = Submit
Part C How much work W3 is done by the gas during step 3? If you’ve drawn a graph of the process, you won’t need to calculate an integral to answer this question. Express the work done in terms of p1, V1, and A. ► View Available Hint(s) ΟΙ ΑΣΦ ? W3W_3 = Submit
Answer
2 Initial pressure (P.), volume of the cylinder. 1 Initial temperature (T) is also given. AP T=0. Hori 3 SD P2 Tz Part A Process 1-2 is isochoric. (AU) =3 ORA for isochove process. P = T2=s Pi Tz API> T2 = A-pi Ti and PV=nRTI. (1) From 1st Law of Thermodynamics, process 1+2 do = two tauSota 32 BR. Ti 2 2,-2 = 3R. 9.2 = 3/4 (3 nR) (T2-T), RTC-1 — 3 2
From equ 1 to 13 and we 091-2 = 35 (A-1 Part – B Process 2-3 (950 Thermal process) (Tz = Ts), work done by Gas during the process to 2-3 know that Internal energy is Furichien of Templ so Au=0 da = aw. Know displacement work (dw), = p.dvItw p.du We We PV = nRT=B = nR7W2-3 = SORT. du 3 V 2 W2-3 hat Jay =? ART (wr7IRT ln (3 ) W2-3= nRT = Pe V2 V2 = nRT2 P2 V2 V2 V2 = 4 P2 = API P2 = 4, P2 = API P2 = 4, Pz= P, fez process P V2= 2P, V3 = 2V and 2u = 2V.
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