PASCO TD-8565 Adiabatic Gas Law Apparatus - Manual (Page 12)

Experiment 3A: Adiabatic Gas Law
© 2009 Physics Enterprises 12
The specific heat at constant pressure, c
P
, is related to the specific heat at constant volume
by
(3.4a)
Thus, a monatomic gas like He or Ar with f = 3 has the ratio γ = [(3/2 + 1)R]/[(3/2)R] = 5/3.
A diatomic gas like the N
2
and O
2
mixture found in air has γ = [(5/2 + 1)R]/[(5/2)R] = 7/5 .
CO
2
has more complex degrees of freedom such that γ = 1.30.
Experimentally, you will determine γ by observing the relation between pressure and
volume. Since Eq. (3.1a), the adiabatic gas law, can be rewritten as
(3.5a)
one sees that a plot of ln(P) vs. ln(V) should be a straight line with a slope of –γ.
R c c
V P
+ =
( ) ( ) ( )
const V P
ln ln ln + − = γ
Procedure
Follow the procedure for the Ideal Gas Law measurements (Experiment I) with two
differences:
A. Insert a pin in the lower hole as an abrupt stop for the piston motion.
B. The gas should be compressed as rapidly as possible to make the experiment
approximately adiabatic.
Analysis
A. Convert voltages to Pressure and Volume as in Experiment I.
B. Use the Calculator to compute the ln(P) and ln(V) and make a graph of ln(P) on the y-axis
vs. ln(V) on the x-axis. Perform a linear fit and record the slope:
Slope = γ = __________
For air, compare this with 1.40.
Repeat the experiment using argon (or helium) and CO
2
comparing with the respective
ratios for these gases.