PC1142 Physics II
The Ideal Gas Law
1
Objectives
• Determine experimentally the ideal gas law governing the pressure P , volume V and
temperature T of an ideal gas.
• Determine an experimental value for the gas constant R.
2
Equipment List
• Gas law apparatus
• Thermometer
• Barometer
3
Theory
Any gas can be described by the macroscopic variables volume V , pressure P and temperature
T . The relationship between these quantities is of fundamental importance. In the most
general case, all of these quantities vary over a wide range and the equation of state that
relates them is inherently very complex. However, if only cases in which the density of the
gas is low are considered, the equation of state is greatly simplified. A gas that satisfies these
conditions is referred to as an ideal gas. Although there are no true ideal gasses, most real
gasses behave to a good approximation as an ideal gas near room temperature and atmospheric
pressure.
In this experiment, we will determine experimentally how P , V and T are related for
the ideal gas. To simplify the investigation, we will look at the behaviour of any two of these
variables, while the third is kept constant. Investigations will be conducted to relate P and V ,
P and T , and V and T . Finally, these relationships will be combined leading to the discovery
of the ideal gas law.
The SI units of pressure P are N/m2 and the SI units of volume V are m3 . In the ideal
gas law, the temperature must always be expressed as the absolute temperature in Kelvins.
The relationship between temperature in Celsius TC and the absolute temperature in Kelvins
T is given by
T = TC + T0
where T0 = 273.15, i.e. the absolute temperature in Kelvin when the temperature in Celsius
is zero.
Physics Level 1 Laboratory
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Department of Physics
National University of Singapore
The Ideal Gas Law
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Figure 1: Gas Law Apparatus.
In this experiment, we will be using the Gas Law Apparatus (see Figure 1) to study the
bahaviours of an ideal gas. The quantity of air, which is to be examined, is held airtight in
a glass measurement tube. The glass measurement tube is connected to a U-shaped mercury
manometer for pressure measurements. The measurement tube is firmly mounted on the high
support, whereas the mercury manometer, consisting essentially of a length of flexible plastic
tubing and an open-top reservoir, can be moved up and down the support in a self-clamping
sliding car. A circulating thermostat can be connected to the jacketing tube surrounding the
measuring tube so that the temperature of the air quantity under test can be varied.
With this Gas Law Apparatus, air can be used as an example to examine the behaviour
of an ideal gas when changes are made in its variables of state: volume V , pressure P and
temperature T . The temperature of the quantity of air which is examined can also be varied
when a thermostat is used as accessory, so that determinations can be made not only on the
connection between pressure and volume, but also on the temperature dependence at constant
pressure (isobaric behaviour) as well as at constant volume (isochoric behaviour).
Physics Level 1 Laboratory
Department of Physics
National University of Singapore
The Ideal Gas Law
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The pressure P in the measuring tube is varied by raising or lowering the mercury reservoir
and the volume V of the trapped air quantity is also varied at the same time. The length of
the column of air in the measuring tube ` and the height difference h between the mercury
level in the reservoir and the level in the measuring tube is read from the scale of the device.
The volume V of the enclosed air quantity is proportional to the length ` of the air column
read from the scale. The volume of the measuring tube segment marked in the brown (cupshaped) can be assumed to be V1 = 1.01 m`. The air volume V2 , up to the lower limit of the
cup-shaped end, is given by
d
V2 = π
2
!2
11.4 mm
`=π
2
2
`
where d is the inner diameter of the measuring tube. The volume V of the enclosed air
quantity is then given by
11.4 mm
V = V1 + V2 = 1.01 m` + π
2
2
`
Figure 2: Determination of pressure in the measuring tube.
The pressure P in the measuring tube consists of two parts, the atmospheric pressure Pa
and any additional pressure, which is called gauge pressure Pg . The gauge pressure Pg is
caused by any height difference h between the mercury level in the reservoir and the level in
the measuring tube,
Pg = ρgh = 0.1333 kN/m2 mm−1 h
The gauge pressure Pg and therefore the height difference h must be given a positive or negative
sign, according to whether the mercury level is higher in the reservoir or in the measurement
tube.
Physics Level 1 Laboratory
Department of Physics
National University of Singapore
The Ideal Gas Law
4
Page 4 of 5
Laboratory Work
Part A: Isothermal Volume Change for An Ideal Gas
In this part of the experiment, you will investigate the relationship between the pressure P
and volume V for the ideal gas at a constant temperature T .
A-1. Determine the atmospheric pressure and record it as Pa in Data Table 1.
A-2. Determine the temperature of the enclosed gas (at room temperature)m in Celsius and
record it as TC in Data Table 1.
A-3. Moving up or down the mercury reservoir to vary the mercury level in the measuring
tube. During this part of the experiment, the temperature in the measuring tube must
be kept constant. Wait until the temperature has become constant before taking any
measurements.
A-4. Determine the height difference between the mercury level in the mercury reservoir and
the level in the measuring tube. Record it as h in Data Table 1.
A-5. Determine the length of the air column in the measuring tube and record it as ` in Data
Table 1.
A-6. Continue varying the mercury level in the measuring tube and repeat steps A-4 and
A-5. Repeat the procedure until EIGHT sets of data have been obtained.
Part B: Isochoric Temperature Change for An Ideal Gas
In this part of the experiment, you will explore the effect of temperature T on pressure P
with the volume V kept constant. A process in which the volume V is kept constant is called
isovolumetric or isochoric.
B-1. Set the desired temperature on the thermostat and wait for temperature constancy in
the measuring tube. Determine the temperature of the enclosed gas in Celsius and
record it as TC in Data Table 2.
B-2. At an initial temperature of TC ≈ 25◦ C, the volume of the enclosed gas corresponding
to the atmospheric pressure P = Pa is determined by lowering the mercury reservoir
until the mercury levels in the measuring tube and the reservoir are at the same height.
Mark this level with a marker on the measuring tube.
B-3. The pressure P corresponding to the respective temperature at a constant volume
(marked volume) is determined from the effective height difference h of the mercury
column. The height difference is read from the scale, after the level of mercury in the
measuring tube has again been brought to the marked initial volume. Record this height
different as h in Data Table 2.
B-4. Raise the temperature in 5◦ C steps until EIGHT sets of data are obtained. Record the
temperature of the enclosed gas in Celsius as TC Data Table 2. For each value of the
temperature, repeat step B-3.
Physics Level 1 Laboratory
Department of Physics
National University of Singapore
The Ideal Gas Law
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Part C: Isobaric Temperature Change for An Ideal Gas
In this part of the experiment, you will explore the effect of temperature T on volume V with
the pressure P kept constant. A process in which the pressure P is kept constant is called
isobaric.
C-1. Set the desired temperature on the thermostat and wait for temperature constancy in
the measuring tube. Determine the temperature of the enclosed gas in Celsius and
record it as TC in Data Table 3.
C-2. To determine the volume of the enclosed gas V corresponding to the respective temperature at constant pressure (P = Pa ), conduct the pressure equilibration in the measuring
tube with atmospheric pressure (level equilibration of the mercury levels in the measuring tube and in the reservoir) and then measure the length of the column air in the
measuring tube. Record the length of the column air as ` in Data Table 3.
C-3. Raise the temperature in 5◦ C steps until EIGHT sets of data are obtained. Record the
temperature of the enclosed gas in Celsius as TC Data Table 3. For each value of the
temperature, repeat step C-2.
Last updated: Sunday 31st August, 2008 1:49am (KHCM)
Physics Level 1 Laboratory
Department of Physics
National University of Singapore