The diagram below represents the P-V change for one mole of an ideal gas. Start
ID: 477837 • Letter: T
Question
The diagram below represents the P-V change for one mole of an ideal gas. Start at P1, V1 and follow the arrows. a. Write an expression for the PV work for each one of the legs in the path. b. Write an expression for the total work done for an ideal gas following the path described by the arrows. c. What is the change in internal energy for the same path? d. What is the value of heat exchanged with the environment for the whole path? Determine whether each of the following thermodynamic quantities is greater than, equal to, or less than zero for the system described. State your reasoning. a) One mole of a monatomic ideal gas is held at a constant temperature of 0 degreeC and allowed to expand slowly against an applied force.Explanation / Answer
Q8
a)
Work for each path:
Path 1,
Volume is the same, pressure changes so:
w = V*dP
W = V1*(P2-P1)
for Path 2:
Constant pressure, so
W = -P*dV
W = -P2*(V3-V2)
for path 3
constant pressure,
W = -P*dV
W = -P3*(V4-V3)
finally
W = V*dP
W = V3*(P3-P1)
b)
Total work done for an ideal gas following the path
So... Total work, sum of all works
Wtotal = W1+W2+W3+W4
Wtotal = V1*(P2-P1) -P2*(V3-V2) + -P3*(V4-V3) + V3*(P3-P1)
c)
by definition, internal energy change in the path is 0, since it is a STATE function
So, it ends up at the same point, so same T, P,V, therefore the same U (internal energ)
d)
Value in the whole path:
Q - W = dU
Since dU = 0
then
Q = W
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