An ideal monatomic gas expands isothermally from state A to state B . It then co
ID: 2251509 • Letter: A
Question
An ideal monatomic gas expands isothermally from state A to state B. It then cools at constant volume to state C. The gas is then compressed isobarically to D where it is then heated until it returns to state A
1.) What is the internal energy of the gas at point B? (Ans: 3x10^3 J)
2.) What is the pressure of teh gas when it is in state B? (Ans: 5 atm)
3.) What is the temp. of teh gas in state C? (Ans: -33 degrees C)
4.) What is the ratio of the internal energy of the gas in state C to that in state A? (Ans: 240/600)
5.) How much work is done on the gas as it is compressed isobarically from state C to state D? (Ans: 400J)
6.) What is the net amount of work done after one complete cycle? (Ans: 1000J)
Explanation / Answer
1)
PA*VA = n*R*TA
n = PA*VA/(R*TA)
= 10*1.013*10^5*2*10^-3/(8.314*327)
= 0.7452 moles
here TB = TA = 327 K
1)
UB = (3/2)*n*R*TB
= 1.5*0.7452*8.314*327
= 3039 J
2)
in iso thermal process
P*v = constant
PA*VA = PB*VB
PB = (VA/VB)PA
= (2/4)*10
= 5 atm
3) at constant volume
P/T = constant
PC/TC = PB/TB
TC = (PC/PB)*TB
=(2/5)*327
= 130.8 K
= -142.2 dgreees
4)
UA/UB = TA/TB
= 327/130.8
= 2.5
5) W = P*(V2-V1) = 2*1.013*10^5*(4-2)*10^-3
= -405.2 J
6)
WAB = n*R*TA*ln(VB/VA)
= 0.7542*8.314*327*ln(4/2)
= +1377.78 J
WBC = 0
WCA = -405.2 J
WDA = 0
Wnet = WAB + WBC + WCD + WDA
= 1377.78 - 405.2
= 972.5 J
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