PASCO TD-8565 Adiabatic Gas Law Apparatus - Manual (Page 14)

Experiment 3B: Work Done by an Adiabatic Process
© 2009 Physics Enterprises 14
Thus, when the gas is compressed adiabatically, we can measure the area under the P vs. V
curve and compare with the change in internal energy given by,
(3.4b)
for an ideal gas with f degrees of freedom.
For the diatomic molecules of air (f = 5) this becomes,
(3.5b)
One can also analytically calculate the area under the P vs. V curve by noting
(3.6b)
where r = V
i
/V
f
is the compression ratio.
T nR
f
U
Δ = Δ
2
T nR Area
Δ =
2
5
( ) ( )
1
1 1 1
1 1 1
1
−
−
= −
−
=
⎥
⎦
⎤
⎜⎜
⎝
⎛
−
− = − = − = − − −
−
∫ ∫ γ γ γ
γ γ
γ γ γ γ
r
V P
V V
V P
V
k
V
dV
k PdV W i i
i v
i i
V
V
V
V
V
V
f
i
f
i
f
i
Procedure
Follow the procedure for the adiabatic gas law measurements (Experiment 3A).
Analysis
A. Convert voltages to Pressure, Volume and Temperature using the Data Studio Calculator
as outlined in Experiment 3A.
B. Construct a plot of Pressure vs. Volume and expand the view appropriately. Using the
Statistics button (Σ), chose Area and record the area under the P vs. V curve.
(Be careful to highlight data that avoids both ends of the P vs. V curve! The numerical
integration breaks down when the ends are included.)
Area = ____________ J
C. Plot Temperature vs. time and use the statistics to record the minimum and maximum
temperature and compute the change in temperature.
T
min
= ____________K T
max
= _____________ K
∆T = ___________ K