PC1142 Physics II. The Ideal Gas Law

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Bernadette Dawson
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1 PC114 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. 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/m and the SI units of volume V are m 3. In the ideal gas law, the temperature must always be expressed as the absolute temperature in Kelvins. The relationship between temperature in Celsius T C and the absolute temperature in Kelvins T is given by T = T C + T 0 where T 0 = 73.15, i.e. the absolute temperature in Kelvin when the temperature in Celsius is zero. Page 1 of 5

The Ideal Gas Law Page of 5 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.

2 The Ideal Gas Law Page of 5 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).

3 The Ideal Gas Law Page 3 of 5 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 l 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 l 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 V 1 = 1.01 ml. The air volume V, up to the lower limit of the cup-shaped end, is given by V = π ( ) d l = π ( ) 11.4 mm l where d is the inner diameter of the measuring tube. quantity is then given by The volume V of the enclosed air ( ) 11.4 mm V = V 1 + V = 1.01 ml + π l Figure : Determination of pressure in the measuring tube. The pressure P in the measuring tube consists of two parts, the atmospheric pressure P a and any additional pressure, which is called gauge pressure P g. The gauge pressure P g is caused by any height difference h between the mercury level in the reservoir and the level in the measuring tube, P g = ρgh = kn/m mm 1 h The gauge pressure P g 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.

4 The Ideal Gas Law Page 4 of 5 4 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 P a in Data Table 1. A-. Determine the temperature of the enclosed gas (at room temperature)m in Celsius and record it as T C 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 l 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 T C in Data Table. B-. At an initial temperature of T C 5 C, the volume of the enclosed gas corresponding to the atmospheric pressure P = P a 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. 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 T C Data Table. For each value of the temperature, repeat step B-3.

5 The Ideal Gas Law Page 5 of 5 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 T C in Data Table 3. C-. To determine the volume of the enclosed gas V corresponding to the respective temperature at constant pressure (P = P a ), 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 l 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 T C Data Table 3. For each value of the temperature, repeat step C-. Last updated: Sunday 31 st August, 008 1:49am (KHCM)

Equation of state of ideal gases

Objective Equation of state of ideal gases F a constant amount of gas (air) investigate the crelation of 1. Volume and pressure at constant temperature (Boyles law) 2. Volume and temperature at constant