Map deal Sapling Learning macmilan leaming A heat engine using a diatomic gas fo
ID: 1055907 • Letter: M
Question
Map deal Sapling Learning macmilan leaming A heat engine using a diatomic gas follows the cycle shown in the p k Pa pV diagram to the right. The gas starts out at point 1 with a volume of 233 cm3, a pressure of 147 kPa, and a temperature of 287 K. The gas is held at a constant volume while it is heated until its temperature reaches 455 K (point 2). The gas is then allowed to expand adiabatically until its pressure is again 147 kPa (point 3) The gas is maintained at this pressure while it is cooled back to its Adiabat original temperature of 287 K (point 1 again) For each stage of this process, calculate in joules the heat Qn transferred to the gas, and the work Wout done by the gas. 147 1 out Step 233 Number Number cm 30.2 Number Number 13.8 Number Number 10.9 27.2 Incorrect. Previous Try Again Next ExitExplanation / Answer
for a diatomic gas, CV= 2.5R
1--->2 work done = 0 for a constnat volume and deltaU= Q = CV*(T2-T10= 2.5*8.314*(455-287)=3492 joules
for constant volume process P1/T1= P2/T2 and P2= P1*T2/T1= 147*455/287=233 Kpa
2--->3 for adiratic expansion, Q=0 and work done =R*(T3-T2)/(Y-1) , Y =CP/CV= 7/5= 1.4 and T1= 455K
T3 = T2*(P3/P2) R/CP = 455*(147/233)2/7 = 399
work done = 8.314*( 399-455)/ 0.4 =-1163.96 Joules
from P2V2Y= P3V3Y
Volume at point 3 = V3= *233*(233/147)1.4 =444 cm3
3--->1 is constnat presure proces for constant pressure, work done = -PdV= -147*(147-444)*0.001 atm.L=4422 joules
Q= deltaH= CP*(T1-T3)= 3.5*8.314*(287-399)=-3269 Joules