1.763.57 The PV diagram below represents 2.70 mol of an ideal menatomic gws. The
ID: 1730694 • Letter: 1
Question
1.763.57 The PV diagram below represents 2.70 mol of an ideal menatomic gws. The gas is inbally at point A. The paths AD and 8C regesant is brought to point C along the path ABC, find the following isothermal changes. I the system (a) the initial and final temperatures of the gas initial 71 inal 88.6 (b) the work done by the gas (c) the heat absorbed by the gas for the work done during an isothermal expansion to find the work done between Use the ideal-gas law to find the temperatures at points A and C Use the expression 8 and C and the first law of thermodynamics to find the heat absorbed by the gas pe here to search 2 abExplanation / Answer
Solution:
From the problem,
a)At A , Using the ideal gas equation,
PV = nRT,
Ta = Td = PV/nR = 4atm*4.01L/2.70*0.082L-atm-K-1 mol-1
= 72.448 K.= 72.5 K
At C, Using the ideal gas equation,
PV = nRT,
Tb = Tc = PcVc/nR = 1atm*20.0L/2.70*0.082L-atm-K-1 mol-1
= 90.33 = 90.33 K.
b)Volume at B,
Vb = nRTb/Pb = 2.7*0.082* 90.33/4 = 5.0L
Work done ABC,
= WA-B + WB-C
= -nR[Tb - Ta] - nRTln[Vc/Vb]
= -nR[17.882 + (90.33ln[20/5])]
= - 3212 J
= - 3.2 kJ.
c)The heat absorbed by the gas,
QA-B + QB-C
= ncp[Tb - Ta] + nRTln[20/5]
= nR[(2.5*17.882) + (90.33*ln[4])]
= 3814 J
= 3.8 kJ.
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