Lecture 3.
Going from one state to another (“thermodynamic transformations”).
In thermodynamics, we will be generally interested in how the system behaves when it
goes from one state to another. This question can be answered if we specify the initial
state (p
i
, v
i
, T
i
), the final state (p
f
, v
f
, T
f
), and the path of the transformation (i.e., the
series of states encountered along the way between the initial and the initial states), as
shown in the figure below.
Note that we plotted our process (it is also referred to as a “thermodynamic
transformation”) in the pV coordinates and we did not indicate on this plot what the
temperature is in the initial and the final state. This is because T is not an independent
variable and it can be calculated from p and
V
by using the equation of state.
To practice doing this, consider the process 1
→
2
→
3
→
1 shown in Figure below.
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Assuming that we are dealing with 1 mole of an ideal gas (so the volume is equal to the
molar volume), we would like to plot the same process in the p&V and V&T coordinates.
pV coordinates:
1
→
2:
Using the equation of state, p = RT/V = R(V/a)/v = R/a = constant. p(1) = p(2) =
R/a. V(2) = V(1) (T(2)/T(1)).
This process takes place at a constant pressure.
Notice that
we needed the ideal gas equation of state to figure this out. If the gas is not ideal then the
conclusion that P is not changed will be wrong.
2
→
3:
pV = RT so that p = RT/V with a constant T).
p(2) = R/a; p(3) V(3) = p(2) V(2);
p(3) = p(2) V(2) /V(3) = p(2) V(2)/V(1) = (R/a) (T(2)/T(1)) = RT(2)/V(1);
This process
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 Spring '11
 Makarov
 Thermodynamics, Heat

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