Expansion process of a perfect gas

 Expansion process of a perfect gas

Asefa Daba Egi(M.Tech)

asefadaba202@gmail.com

Ethiopian Defence University, College of Engineering, Ethiopia

 Contents

1.   Introduction. 1

2.   Objectives. 2

3.   Theory. 2

4.    General Start-up Operation. 3

4.1  Operational Procedure. 4

5.    Observation tables. 4

6.    Question to be answered. 5

1.     Introduction

The perfect gas expansion apparatus is a self-sufficient bench top unit designed to enable students to familiarize with some fundamental thermodynamic processes. Comprehensive understanding of first law of thermodynamics, second law of thermodynamics and the P-V-T relationship is fundamentally important in the applications of thermodynamics in the industry. The apparatus comes with one pressure vessel and one vacuum vessel and both are made of glass tubes. The vessels are linked to one another with a set of piping and valves. A large diameter pipe provides gradual or instant change. Air pump is included to enable us to pressurize or evacuate air inside the large vessels provided the valves configures appropriately during the experiment. The pressure and temperature sensors are used to monitor and manipulate the pressure and temperature inside the vessels and the digital indicator will display the pressure and temperature on the control panel. This experiment dealt a lot with the properties of an ideal gas and its relationship with the various environmental factors. An ideal gas is said to be a gas which obeys the P-V-T relationship. A PVT relationship is one of the forms of the equations of state, which relates the pressure, molar volume V and the temperature T of physically homogeneous media in thermodynamic equilibrium (Reid, Prausnitz & Sherwood, 1977). 

Other than that, ideal gas is also a gas that exhibits simple linear relationships among volume, pressure, temperature and amount (Silberberg, 2007). Gas particles in a box collide with its walls and transfer momentum to them during each collision. The gas pressure is equal to the momentum delivered to a unit area of a wall, during a unit time. However, ideal gas particles do not collide with each other but only with the walls. A single particle moves arbitrarily along some direction until it strikes a wall. It then bounces back, changes direction and speed and moves towards another wall. The gas expansion equations are derived directly from the law of conservation of linear momentum and the law of conservation of energy (Sears & Salinger, 1975).

2.    Objectives

1. To verify Gay-Lussac Law (To determine the relationship between pressure and temperature of an ideal gas)

2. To study the response of the pressurized vessel following stepwise depressurization   

3. To study the response of the pressurized vessel following a brief depressurization.

3.     Theory

Gay-Lussac Law Experiment

Gay-Lussac law is also commonly known as Charles’s law. The law explains about the relationship between pressure and temperature of gases. The law was established in the early19th century by Jacques Charles and Joseph Louis Gay-Lussac who did a study on the effect of temperature on the volume of a sample of gas subjected to constant pressure (Atkins, 2002). Charles did the original work, which was then verified by Gay-Lussac. However, in this lab practical, we are dealing with an alternative version of Charles’s law instead. The volume is kept constant in change for pressure instead as the objective of the experiment is to determine the relationship between pressure and temperature of ideal gas. The expression is shown as:

p = constant x T (at constant volume)

*This version of law also indicates that the pressure of gas falls to zero as the temperature is reduced to zero (Atkins, 2002). 

Thus it can be seen that gas pressure and the temperature are directly proportional to one another. When the pressure increases, the temperature also increases, and vice versa.

P ∝ T

P = at constant T

P/T = constant

P1/T1 = P2/T2

P1T2= P2T1

Where; P1 is the initial pressure

      T1 is the initial temperature

      P2 is the final pressure

      T2 is the final temperature

 The equations above apply in the gas of dealing with the relationship between pressure and temperature of a gas.


Figure1: Graphical relationship between pressures of a fixed mass of gas with temperature at a constant volume is linear.

Stepwise Depressurization Experiment

The stepwise depressurization is conducted by depressurizing the pressurized chamber or tank gradually by releasing the gas expansion at every instance the valves are opened and closed to see the gradual changes in pressure within the container. Pressure decreases with the expansion.

Brief Depressurization Experiment

Similar procedures as previous lab practical, but the time interval of valves opening increased to a few seconds. This is so that the effects or response of brief depressurization of the gas could be observed. With the increased time interval, the gas should expand faster.

Apparatus 

  • S.P. ENGINEERS model

4.        General Start-up Operation

a.             The equipment is connected to single phase power supply and then turn on switch.
b.             Fully open all the valves and check pressure reading on the panel. This is to make sure that the chambers were all under atmospheric pressure.
c.                Close all valves again afterwards.
d.                  The pipe from compressive port of the pump is connected to pressurized chamber.
e.                   The unit was ready for use.

4.1      Operational Procedure

1.      Perform general startup method again.

2.      Connect the hose from compressive pump to pressurized chamber

3.      Switch on compressive pump and record temperature every increment of 0.1kpa pressure in the chamber.

4.      Then open the valve slightly and allow pressurized air to flow out.

5.      Record the temperature reading for every decrement of 0.1kpa pressure (stepwise experiment).

6.      Stop the experiment when pressure reaches atmospheric pressure

7.      Pressurize the tank again and do the brief depressurization experiment.

8.      Repeat the experiment  to  get proper data

9.      Plot the graph of pressure vs temperature

5.      Observation tables

Test A: Pressurization

s/n

Pressure1

pressure 2

Temperature 1

Temperature2

1

 

 

 

 

2

 

 

 

 

3

 

 

 

 

5

 

 

 

 

6

 

 

 

 



 

 

Test B: Depressurization       

s/n

Pressure1

pressure 2

Temperature 1

Temperature2

1

 

 

 

 

2

 

 

 

 

3

 

 

 

 

5

 

 

 

 

6

 

 

 

 



 

 

 6.                  Question to be answered

  1.                  Plot temperature vs pressure for pressurization.
  2.             Verify Gay-Lussac’s Law.
  3.                  Plot temperature vs pressure for depressurization.
  4.                   What you understand from this experiment?

Bibliography

  1.  Reid, R., Prausnitz, J.M., and Sherwood, T.K. (1977) The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill.
  2.  Martin Silberberg, 2007, Principles of General Chemistry, 1st Edition, McGraw-Hill
  3.  F.W. Sears, G.L. Salinger, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (Addison-Wesley, 3rd ed 1975) pp 254-266, 354-360.
  4. Peter Atkins & Julio de Paula, 2002, Physical Chemistry, 7th Edition, Oxford, Page 8- 10, 92 & 103. 


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