The state of an ideal gas can be represented by a point on a PV (pressure-volume
ID: 1379840 • Letter: T
Question
The state of an ideal gas can be represented by a point on a PV (pressure-volume) diagram. If you know the quantity of gas, n, a unique point in pressure (P) and volume (V) can be used to determine a temperature (T). Each point on a PV diagram also has a single internal energy (U) assigned to it. If a process starts at a point and returns to that same point on a PV diagram, it returns to the same P, V, T, and U.
The PV diagram below shows four different states, A, B, C, and D. The lines connecting the states represent processes or transitions. For example, the line connecting states A and B represents an expansion of the gas (transition to larger volume) while the pressure is kept constant. In the case of this diagram, the pressure at states A and B is 3.80?105 Pa. The pressure at states C and D is 1.44?105 Pa. Likewise the volume at states A and D is 1.40?10-3 m3 and the volume at states B and C is 4.48?10-3 m3.
What is the work done by the gas for the transition BC?
What is the work done by the gas for the transition AB?
What is the work done by the gas for the transition CD?
What is the change in internal energy, ?U, if you follow the system all the way from A to B to C to D and back to A?
B A D PExplanation / Answer
What is the work done by the gas for the transition BC?
No change in volume of the gas, then
WBC = 0
What is the work done by the gas for the transition AB?
WAB=p1(VB-VA) = 3.8x105 Pa * (4.48-1.4)x10-3 m3= 1170.4 Pa.m3 = 1170.4 Jouls
What is the work done by the gas for the transition CD?
WCD=p2(VD-VC) = 1.44x105 Pa * (1.4-4.48)x10-3 m3= -443.52 Pa.m3 = -443.52 Jouls
What is the change in internal energy, ?U, if you follow the system all the way from A to B to C to D and back to A?
If the system experiences a cyclical transformation, the change in internal energy is zero, and that the state A and returns to the same state, ( Delta U = 0)
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