Question

An engine works on the cycle shown in the diagram below, using 0.1 moles of a monatomic ideal gas. The processes A, B and C are isothermal, isovolumetric and adiabatic respectively. The maximum and minimum volumes are 8 litres and 2 litres, and the temperatures are as shown on the diagram. T=1000K Pressure (kPa) T=397K 0 8 2 4 6 Volume (litres) a) b) c) d) e) Calculate the work done on the gas in processes A and B. Calculate the heat transferred to the gas in processes A, B and C. Hence calculate the work done on the gas in process C. Hence calculate the efficiency of this engine. What is the efficiency of the best possible engine operating between reservoirs at the same maximum and minimum temperatures? Calculate the pressure at the beginning of process C (or, equivalently, at the end of process B). f)

Answer 1

€0:81 67-01-610C w Sol Toon 100 Teet T14 (ca) Work done on a gas in process A and it Process Ai- Since the process A is isothermal ( conste temperature) for this process is done 13 process, the work given by AN 2.303 n RT log where n = no. of moles - Temperature - maximum vol. = feral volume vi minimum vol - Intal volume AOW- -(2,303) 0:1260.002.1) (1000) log - (18.9) logy = +18.9) 10.602) 11.38 Latm

Page: Date: process Bi- Since process B is tsochoric (constant volume) process, therefore, the work done in this process is zero Because, work done in Isochoric process is given by to W=pAV Since Av=o A and b) Heat transterred and Gia Terred to to the the gas in gas in A,B AB is othermal ork done process A - Using 1st how of thermod Isothermal) DQ = AU + AW where AQ 2 Heat tranferred Au Change in internal energy - DWZ work doneo ve volume Since in isothermal process Auzo because ou = CVAT = 0 as AT=0. 2. AO = AW is AO = 11.38 Latman Process Bi-([sochoric) - To Using 1st law agai - AU+ w Since AW-o in isu 2019-10-29 18:04

Page therefore, oor or so= nCAT Where Cv a specific heat at volume Constant Now, Cr can be written in terms of known quantities like R and r Ri gas Constant and r= Ses Now, Cuz R Y- of Cra 0.124 0.0821 leff- value of monoatomic molecules. AQ = (0.1) Co. 124) (397-1000) = -7.47 لالها Process In ci- (Adiabatic process) adiabatic process, AQ=0 (CC) work done on the gas in Process In process cladiabatic the work done on the process C!- process), gas is given by 2019-10-29 18:04

2019-10-29 18:07 W = MR C w (o.l) (0.0821) (1000-397) lift 1) 7.5 Latm iciency of engine! - Total work done un gas Total heat transferred 11-387 75 100 to 28+ (67.47 ( not sure about this part) .47