College Physics Lab
PH 141
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Ideal Gas Law

Purpose: To verify the ideal gas law for a constant temperature (Boyle's Law), and thereby determine the gas constant R.

Discussion: The ideal gas law relates the pressure P, volume V, and (absolute) temperature T through the relationship PV = NkT, where N is the number of particles of gas and k = 1.38*10-23 J/K is Boltzmann's constant. Rearranging the ideal gas law as

P = (NkT)/V

we can see that if N and T are constant, P is proportional to 1/V (Boyle's law).

The following symbols are used:
 
P = absolute pressure of the gas Patm = atmospheric pressure
M0 = mass of the syringe plunger and block M = mass on top of the plunger
A = cross-sectional area of the syringe r = inner radius of the syringe
V0 = initial volume
N = number of particles of air NA = Avogadro's number = 6.02 X 1023

 
Procedure:
1. Measure M0. Using vernier calipers, measure the inner diameter of the syringe and calculate the radius r. Calculate A = pr2 in m2.

2. Insert the plunger into the syringe until you have approximately 25 cm3 of air trapped. You may use the thin wire to release some air if necessary. Insert the plunger slowly; allow the pressure inside the syringe to equalize with room pressure (atmospheric pressure = 101 kPa).

3. Measure V0 to the nearest 0.1 cm3 or 0.2 cm3.  Calculate N. Assuming that 22.4 liter of gas at standard temperature and pressure (STP) contains NA gas molecules, construct a proportion that allows you to determine the approximate number of gas molecules in your syringe. Recall that 1 liter = 1000 ml.

4. Position the syringe so that weight may be placed on top of the plunger, i. e. the air will be compressed. Beginning with M = 0, measure V to the nearest 0.1 cm3 as M is increased in 0.5 kg increments. You might find it useful to twist carefully the plunger a little back and forth in order to keep it from sticking.

5. For each M and V, calculate the pressure acting on the air in the syringe from,
P = Patm + (M0 + M)g/A .

6. Make a graph of P vs 1/V. Find the slope of your best line through the data. Knowing N and T, calculate k from your slope. Compare your empirical value to the accepted value.