Gas Laws. Topics for Discussion Relationship Between Heat and Volume

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1 Gas Laws Topics for Discussion Relationship Between Heat and Volume Relationship Between the Properties of Gases Constant Temperature Processes Constant Pressure Processes Constant Volume Processes Avogadro s Law The Ideal Gas Law

2 The Relationship Between Heat and Volume Changes in the internal energy of a substance produce corresponding changes in its volume. When a transfer of thermal energy increases the internal energy of an uncontrolled substance, two reactions typically occur. The thermal energy transfer increases the temperature and volume of the substance.

3 The Relationship Between Heat and Volume The rise in temperature is a consequence of the increase in kinetic energy. The increased volume occurs in response to an increase in potential energy that appears as an increase in the distance between the molecules. Conversely, when energy is transferred from a substance, it contracts as temperature reduces.

4 The Relationship Between Heat and Volume Tremendous pressures are created whenever a substance in its solid or liquid phase is restrained or confined so that its volume is not permitted to change in response to changes in its temperature. To provide for the normal expansion and contraction of materials that is driven by changes in temperature, expansion joints are utilized in various structures.

5 Coefficient of Expansion When solids and liquids are heated and their temperatures increases, their volumes also change a fixed quantity for each on degree rise in temperature. The coefficient of expansion differs among different materials. It is also known to vary for the same substance, based on the temperature at which the heat transfer is occurring.

6 Paradox of Water One of the few exceptions to the direct relationship between temperature and volume is water. As warm water is cooled, its volume decreases as expected, until its temperature drops to 39.2 F. At this temperature water achieves its maximum density, and smallest volume.

7 Paradox of Water As the water cools past 39.2 F it begins to expand, this expansion continues as long as the temperature continues to drop toward it s triple point 32 F. At the triple point temperature, the liquid water begins to change phase into a solid, continuing to expand. 1 ft3 of water will freeze to ft3

8 Paradox of Water Although the expansion of water appears to contradict the temperature-volume relationship this is not the case. The average distance between the cooling molecules continues to decrease as the temperature drops. But a physical rather than a thermal expansion occurs as the water molecules arrange into a crystalline structure.

9 Relationship Between The Properties of Gases The reaction of gases to changes in thermal energy is much more complex than that of liquids and solids. This complexity requires the use of several equations to determine their properties. The change in volume experienced by gases as they are heated or cooled is much greater than that experience by solids or liquids.

10 Relationship Between The Properties of Gases The complexity of the change is a consequence of the lack of structure and weak molecular attractions of gas molecules as compared to those of solids and liquids. Therefore, several gas laws were developed that are used to predict the response of a gas to changes in its environment.

11 Relationship Between The Properties of Gases Through the application of these gas laws, technicians can predict the response of refrigeration processes that use gases and vapors as their working fluids. Remember that a gas completely fills its containing vessel so that any change in volume produces corresponding changes in its temperature and pressure. The following equations are for constant processes.

12 Constant Temperature Processes In 1662, Robert Boyle determined that if the temperature of a gas was kept constant, changes in its absolute pressure and volume were indirectly related to each other. When a constant temperature gas was compressed, its absolute pressure increased in proportion to the reduction in its volume.

13 Constant Temperature Processes Conversely, when a gas was expanded at a constant temperature, its absolute pressure decreased in proportion to the increase in its volume. This discovery led to the publishing of the first of three ideal gas laws. The law is named after Robert Boyle and is called Boyle s law for constant temperature processes.

14 Constant Temperature Processes Any thermodynamic process that occurs in such a manner that the temperature of the working fluid is held constant, is called an isothermal process. Since the molecules of any gas fly about randomly at high velocities, they frequently collide with one another and with the walls of their container.

15 Constant Temperature Processes Billions and billions of gas molecules strike the interior walls at any instant in time. It is these molecular collisions that manifest themselves as pressure exerted on the walls of the containment vessel. The magnitude of the pressure generated by a gas is a function of the frequency and the force of the molecular impacts.

16 Constant Temperature Processes There are several processes, that can increase the pressure of a gas. When the number of molecules contained in a volume of gas is increased, the number of collisions also increases, this increases the pressure in the vessel. The same reaction occurs when the number of molecules remains the same but the volume decreases.

17 Constant Temperature Processes Engines and compressors are used to raise gas pressure by trapping a fixed amount of gas in a cylinder and reducing the volume by moving a piston toward the cylinder head. As the piston reduces the volume available for the gas, raising the number of molecular collisions and the pressure in the cylinder.

18 Constant Temperature Processes Another process that can be used to raise the pressure of a confined gas is transferring heat to the vessel. Since the force created by the molecule colliding with its vessel s wall is a function of its velocity, raising the molecular velocity is accomplished by raising its kinetic energy.

19 Constant Temperature Processes The higher the temperature, the greater the molecular velocity and the forces transmitted during collisions with the vessel walls. In isothermal processes, the temperature and its kinetic energy remains constant. Therefore, differences in pressure can only occur if the volume or the mass of the gas within the vessel is altered.

20 Constant Temperature Processes In accordance with Boyle s law, if a gas is allowed to expand in a constant temperature process, changes in its volume and pressure are inversely related. Since the kinetic energy of the gas remains constant in isothermal expansion processes, the decrease in pressure is the result of the reduction in density of the gas as it expands to fill the volume of the containment vessel.

21 Constant Temperature Processes The decrease in density reduces the frequency of molecular collisions, producing a corresponding decrease in the gas pressure. Since gas cools as it expands, the isothermal characteristic of the process can only be maintained if heat is transferred to the gas during an isothermal expansion process.

22 Constant Temperature Processes The complementary response of an expansion process occurs when a gas is isothermally compressed. When a gas is compressed at a constant temperature, the pressure increases in proportion to the magnitude of the decrease in gas volume.

23 Constant Temperature Processes The reduction in volume of the containment vessel causes a corresponding increase in the density of the gas. As the density of the gas increases, the frequency of collisions also increases, generating a corresponding increase in pressure.

24 Constant Temperature Processes The average velocity and kinetic energy of the molecules must remain unchanged in order to maintain the relationship of Boyle s law. Therefore, heat must be transferred from the cylinder during an isothermal compression process.

25 Constant Pressure Processes In 1787 Jacques Charles discovered that if the pressures of carbon dioxide, hydrogen, oxygen and nitrogen were kept constant, they expanded at predictable rates in response to an increase in their temperature. Charles never published his findings, still this relationship is called Charles law for constant pressure processes.

26 Constant Pressure Processes Any thermodynamic process that occurs in such a way that the pressure of the working fluid is held constant is called isobaric process. As thermal energy is added to the gas, its temperature and volume increase in accordance with Charles law. The heat transferred to the gas increases its kinetic energy and the velocity of its molecules.

27 Constant Pressure Processes The higher energy collisions increases the pressure within the cylinder, consequently the volume must expand to maintain the constant pressure relationship. Heat must be transferred to or from the cylinder in an isobaric process in order to maintain the relationship between volume and temperature, as described in Charles law.

28 Constant Pressure Processes When thermal energy is removed from the cylinder, the pressure in the cylinder begins to decrease. The volume of the cylinder must then be decreased to maintain the constant pressure relationship.

29 Constant Volume Processes Charles explored the relationship between temperature and pressure in constant volume processes. He found that when the volume of a process remains constant, the pressure of the gas changes in direct proportion to the change in its temperature. Once again Charles never published his findings

30 Constant Volume Processes In 1802 Joseph Gay-Lusaac repeated Charles gas experiments as he studied gases. His findings agreed with the earlier unpublished work of Charles. Gay-Lusaac published his data in 1809, and for that reason Charles law of Constant Volume Processes is also known as Gay-Lusaac s law.

31 Constant Volume Processes Any thermodynamic process that occurs in such a way that the volume of the working fluid is held constant is called an isometric process. In a constant volume process the volume of the gas cannot change as it is heated or cooled, therefore changes in the pressure can only be caused by changes in its temperature.

32 Constant Volume Processes As heat is added to the cylinder, the absolute pressure of the gas increases in direct proportion to the increase in the absolute temperature of the gas. The response occurs because the addition of heat increases the kinetic energy and velocity of the gas molecules, thereby increasing the force transmitted to the cylinder walls by molecular collisions.

33 Constant Volume Processes Conversely, when the gas in the cylinder is cooled, its absolute pressure decreases in direct proportion to the decrease in absolute temperature. This occurs because the force and frequency of molecular impingement on the walls of the cylinder diminish as their velocity decreases.

34 AVOGADRO S LAW In 1811, Amedeo Avogadro proposed that equal volumes of different gases contain the same number of particles when maintained at the same pressure and temperature. It was later discovered that a volume of 0.79 ft3 at 32 F and psia contains approximately 6.02 x or 602 billion trillion particles

35 AVOGADRO S LAW This number is called the Avogadro constant, and is used as a measurement of quantity in combustion analysis, gas measurements and other chemical analysis. This quantity is called a mole of a substance, one mole of any substance contains 6.02 x elementary particles (atoms, molecules, ion, electrons, etc.)

36 AVOGADRO S LAW The symbol for Avogadro constant is a lowercase letter n Moles are measured in mass units (lbmol, kgmol)

37 The Ideal Gas Law The ideal gas law was developed by combining the relationships in Boyle s and Charles laws along with Avogadro s number into a single formula. Combining Boyle s and Charles laws yields the following equation = This on equation is all that is needed to solve Boyle s and Charles law relationships.

38 Specific Gas Constant A gas constant is a property of a gas that expresses the relationship that exists between its absolute temperature, absolute pressure and volume at a given state. The gas constant is a calculated value equal to the product of the absolute pressure and specific volume of the gas divided by its absolute temperature.

39 Specific Gas Constant The result is known as the specific gas constant of the gas and is depicted with an uppercase R. = = Imperial = = Metric

40 Specific Gas Constant The mathematical result of the formula is always the same for a particular gas because increases in its absolute pressure and temperature are offset by a corresponding decrease in its specific volume. The specific gas constant is an extensive property of a gas, meaning its quantity is based on a unit mass of gas.

41 Universal Gas Constant A universal gas constant is a property of gasses that has the same value. The universal gas constant is equal to 1545 ft-lbf/lbmol-r or 8,314 J/kgmol-K. The symbol for the universal gas constant is *R where the asterisk indicates the universal value is being used in the equation.

42 Universal Gas Constant The universal gas constant is based on the quantity relationship of gas molecules discovered by Avogadro. Since there are equal numbers of particles in one mole of a gas at a given volume, temperature, and pressure, the only difference between gasses must be caused by differences in the configuration of their atoms.

43 Universal Gas Constant The only difference between gases happens to be in the makeup of their molecular structure, which is depicted in their mass or molecular weight. The molecular weight of an atom is equal to its atomic number, which is found on the periodic table of elements.

44 Universal Gas Constant The specific gas constant of a gas can be calculated by dividing the universal gas constant (*R) by the molecular weight of a one mole quantity of a gas. Oxygen has a molecular weight of 32, therefore, its specific gas constant is equal to = 48.3 lbf/lbm R

45 Ideal Gas Gases are highly superheated vapors. A gas is considered to behave in an ideal manner when its pressure is very low and its temperature is considerably higher than its critical temperature. The critical temperature of a substance indicates the highest possible temperature at which the substance can exist as a liquid.

46 Ideal Gas Above the critical temperature there is no longer any difference between the properties of its liquid and gas phases At psia oxygen liquefies at -297 F, as its pressure is raised to 750 psi it can be liquefied at F. Therefore, this is also the highest temperature at which the gas can be condensed.

47 Ideal Gas F is the critical temperature for oxygen. If oxygen exists at a temperature that is much greater than F, it will behave as an ideal gas, thereby adhering to Boyle s and Charles laws. Conversely refrigerants do not behave as ideal gases because they exist at temperatures that are too close to their saturation temperatures.

48 Ideal Gas Their molecules are packed much closer and, consequently they experience too much interaction between their electrostatic forces. This produces the molecular equivalent of friction, since the effects of friction cannot be reversed, the vapor and its process are not ideal.

49 Ideal Gas Therefore, the process and the gas cannot be adequately described using the relationships described in Boyle s, Charles and the ideal gas laws. The analysis of processes using non-ideal gases must be performed using property tables to determine their condition at specific states.

Module 5: Rise and Fall of the Clockwork Universe. You should be able to demonstrate and show your understanding of:

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