# Relationship between Pressure and Temperature Kinetic Theory

Relationshipbetween Pressure and Temperature: Kinetic Theory

Relationshipbetween Pressure and Temperature: Kinetic Theory

Aim

Investigatingthe relationship between pressure and temperature

Thekinetic theory of gases contains certain postulates upon which themodel is described they are as follows:

1. A gas is composed of molecules sparsely populating a region of space.

2. The molecules of a gas are in a rapid motion and frequently collide with each other and the walls of their container.

3. The collisions area assumed to be perfectly elastic. From the mechanical standpoint, the molecules suffer no loss of momentum as a result of their collisions although momentum can be transferred from one particle to another.

4. Temperature is directly related to the average kinetic energy of the molecules. The pressure a gas exerts is the result of the average force of the repeated collisions of the molecules with the walls of a container.

Hence,the higher the temperature, the greater the kinetic energy. Thetheoretical relationship between absolute temperature and kineticenergy of the molecule is

Wherenis the number of molecules, and the other terms are identical tothose in the general kinetic energy formula

Ifenergy (or temperature) of a gas is increased, the force exerted bythe molecules as the molecules also bombard with the walls of acontainer also increase. This increased results in an increasedenergy results in an increased pressure, and we can experimentallyarrive at Amonton’s Law: pressure and temperature vary directlywith each other at constant volume.

Procedure

1. Place a two-liter beaker on the ring stand over the laboratory burner. The beaker should contain just enough water to cover the bulb of the pressure-temperature apparatus when the bulb is placed inside. Heat the water to boiling.

2. In another two-liter beaker, place enough chipped ice and water just to cover the pressure bulb.

3. A third beaker should contain an acetone-dry ice mixture (to obtain a temperature of about -70 degrees Celsius)

4. If it is available, use a Dewar flask containing liquid nitrogen (temperature of about -196 degrees Celsius).

5. Read and record the pressure in the bulb at room temperature.

6. Now read the pressure of the gas in the bulb when it is placed in each of the other three containers and record the pressure and temperature of each.

Results

Table1

 Temperature (°c) Temperature (K) Pressure (lb/in2) 4.0 277.0 13.31 23.0 294.0 14.30 70.0 350.0 17.52 100.0 373.0 17.28 196.0 496.0 20.78

Theabove table represent data collected during the experiment, A graphof temperature against pressure was plotted, and it’s representedas follows

Temp (°C)

Pressure lb/in2

Graph1.Plottingtemperature against pressure

Discussion

Calculationsand Questions

1. Heating the bulb increases the pressure inside the bulb.

2. The relation between the temperature and the pressure is that they are a linear relation, doubling temperature will not double the pressure. For instance, -200°C which indicates a 125°C increase for lowest attainable temperature according to the graph, this corresponds to 5 lb/in2, when we double the temperature to -75°C so that we indicate an increase of 250°C increase, this corresponds to 16°C.

3. According to the graph above, -325°C is the temperature at which the pressure will be zero. At this temperature, no molecules would be moving hence there is no collision between gas particles. According to the Kinetic Theory, no pressure is exerted on the bulb’s walls.

4. The graph plotted cuts the x-axis at -325°C, which is way below the Absolute Zero temperature (273°C). Hypothetically, no matter can be colder than absolute zero on a Kelvin scale.

 Temperature(°C) Pressure (PSI) Temperature (K) 23°C room temperature 14.7 296 50 16.0 323 100°C Boiling water 18.5 373 -5° Ice & salt water 13.3 268 -70 Acetone dry ice 10.1 203

Theabove

423K

Temp (°C)

Pressure (PSI)

373K

273K

223K

323K

173K

123K

73K

23K

Graph2-plottingtemperature against pressure

Calculationsand Questions

1. According to kinetic theory: Gas pressure is due to the molecules colliding with the walls of the container, Gases consist of particles in constant, random motion.

2. 73K corresponds with 4 PSI, while 146 with 8 PSI, thus when we double the temperature, pressure also doubles. This kind of relation is called direct linear variation.

1. According to Graph2 above, approximately -273°C is the temperature at which the pressure is zero. This temperature is known as the absolute zero point. At this temperature, no molecules would be moving around hence there is no collision between gas particles. No pressure is exerted to the walls of the bulb. This is according to the Kinetic Theory.

1. The value (-273°C) which is also 0 Kelvin, corresponds with the standard of the Kelvin scale, indicating that as the lowest temperature attainable.

Conclusion

Overall,the experiment was successful in showing that the temperature andpressure of an ideal gas at constant volume and mass follows therelativity of the ideal gas equation. Differences can be accountedfor by experimental error.