Question

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

Answer 1

Given 2 Initial pressure (P.) = 1 Initial temperature =T, volume of cylinder Pressure after heating = AP T=0 add Hori 3 V SD P2 Tz T Part A Process 1-2 is isochoric, i-e dvso oisplacement work (otw) = p.dv=0 Internal energy change for mono a tonic gas is given as (AU) = 3 ORA for iso chove process P = P2 = T2 = स Pi Tz API > T2 = A - pi Ti and PV=nRTI (Gas equation) - (2) from 1st law of Thermodynamics for process 1+2 do = two tau Sota 32 BR dt Ti 2 2,-2 = 3R (7) ? 9.2 = 3/4 3 nR (T2-T) RTC-1) -- 3 2

get from equ ① and 2 and 13, we 091-2 = 35 (A-1) Part - B Process 2-3 (950 thermal process) ( Tz = Ts) work done by Gas during process to 2-3 know, Internal energy is furichien of Templ only so Au=0 da = aw for this process. know displacement work (dw) = p.dv Itw p. du We We 2 PV = nRT = B = nR7 W2-3 = SORT. du 3 V 2 W2-3- hat Jay =) ART (wr7 IRT ln ( 3 ) W2-3 = nRT = nRT2 = P2 V2 Pe V₂ = nRT2 W2-3 = P V z ln ( 2 ) P₂ = API V₂ = 4, Pz = P, fez isothermal process P V₂ = 2P, V V3 = 2V, ₂ų = P22 SO W2-3 Apy, ln (2v, W2-3 Apiv, lna