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The figure(Figure 1) shows a thermodynamic process followed by 110 ng of helium. You may want to review (Page 515)
For help with math skills, you may want to review:
Conversion Factors
Conversion Between Celsius and Kelvin
Rearrangement of Equations Involving Multiplication and
Figure
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Part A Determine the pressure (in atm) of the gas at points 1, 2, and 3
p1,p2,p3 = 0.999,5.0,0.999 atm
Part B Determine the temperature (in °C) of the gas at points 1, 2, and 3
T1,T2,T3 = °C
Part C Determine the volume (in cm3) of the gas at points 1, 2, and 3.
V1,V2,V3 = cm3
Part D How much work is done on the gas during each of the three
W1→2,W2→3,W3→1 = J
Part E How much heat energy is transferred to or from the gas during each of the three segments?
Q1→2,Q2→3,Q3→1 = J
♦ Relevant knowledge
The first law of thermodynamics states that any change to inner energy that the system produces is proportional to the amount of heat transferred or added plus the work that is done in the course of the system.
ΔU=Q−W
The S.I unit of energy is Joules (J).
m = given mass = 110 mg = 0.110 g
M = molar mass = 4 g/mol
N = Number of Moles
n = M/M = 0.110/4 =0.0275
Part A
Point 1:
T 1 = Temperature At Point 1 = 133C = 133 + 273 = 406 K
V 1 = Volume At Point 1 = 1000 cm = 10 -3 M
P 1 = Pressure at Point 1 =?
Use the equation
P1 V1 = n R
T1
Inserting the values
P1 (10-3 ) = (0.0275) (8.314) (406)
P1= 92825.8 p = 0.916
atm
Point 2:
P2= 5 P1 = 5 (0.916) = 4.58 atm
Point 3:
P3 = P1 = 0.916
atm
Part B)
T1 = 133 oC
Process 1 and 2:
P1/T1 =
P2/T2 (Since volume is constant)
P1/(133 + 273) = 5P1/T2
T 2 = 2030K
T2= 2030 – 273 = 1757
oC
T3 = T2 = 1757
oC
Part C
V1 = 1000 cm3
V2= V1 = 1000
cm3
V1/T1 = V3 /T3
1000/(133 + 273) = V3 /2030
V3 = 5000 cm3
Part D
for process 1-2 :
W1-2= P1-shows-a-thermodynamic-process-followed-by-110-ng-of-helium..png?x-oss-process=image/resize,w_560/format,webp)
V = 0
for process 2-3 :
W 2-3 = N R T 2 log (V 3/V 2).
W2-3= (0.0275) (8.314) (2030) log(5000/1000) = 747 J
for process 3-1:
W3-1= P1 (V1 – V3) = (92825.8) (0.001 – 0.005) = – 371.3
J