PASCO TD-8572 HEAT ENGINE_ GAS LAW APPARATUS - Manual (Page 21)

012-06014C Heat Engine/Gas Law Apparatus
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b. On the graph in part a, label each of the points on the cycle (a, b, c, and d). Indicate on
the graph which of the transitions (a ➔ b, b ➔ c, etc.) are adiabatic and which are isobaric.
Next you need to find a way to determine the area enclosed by the P- V diagram. The
enclosed area doesn't change very much if you assume that P is approximately a linear
function of V for the adiabatic transitions. By making this approximation, the figure is
almost a parallelogram so you can obtain the enclosed area using one of several methods.
Three of the many possibilities are listed below. Creative students have come up with even
better methods than these, so you should think about your method of analysis carefully.
Method I
Since the pressure doesn't change from point b to point c, you can take the pressure of
those two points as a constant pressure between points. The same holds for the transition
from d to a. This gives you a figure that is approximately a parallelogram with two sets of
parallel sides. You can look up and properly apply the appropriate equation to determine
the net thermodynamic work performed.
Method II
Display your graph with a grid and count the boxes in the area enclosed by the lines
connecting points a, b, c, and d. Then multiply by the number of joules each box repre-
sents. You will need to make careful estimates of fractions of a box when a "leg" of a
cycle cuts through a box.
Method III
PdV = PdV
a
b
+ PdV
b
c
+ PdV
c
d
+ PdV
d
a
Fit a straight line to each of the starting and ending points for the four transitions in the
cycle. Each equation will give you a function relating P and V. Perform an integral for
each of these equations, since
5.5 Activity: Comparing the Thermodynamic and Useful Mechanical Work
a. Choose a method for computing the thermodynamic work in joules, describe it in the space
below, and show the necessary calculations. Report the result in joules.