Charles law

10 Key excerpts on "Charles law"

• 

  No longer available |Learn more

  Laws and Theories of Thermodynamics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  which can be written as: where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully expressed as follows: The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion. Limitations In modern physics, Charles' Law is seen as a special case of the ideal gas equation, in which the pressure and number of molecules are held constant. The ideal gas equation is usually derived from the kinetic theory of gases, which presumes that molecules occupy negligible volume, do not attract each other and undergo elastic collisions (no loss of kinetic energy); an imaginary gas with exactly these properties is termed an ideal gas . The behavior of a real gas is close to that of an ideal gas under most circumstances, which makes the ideal gas law useful. This law of volumes implies theoretically that as a temperature reaches absolute zero the gas will shrink down to zero volume. This is not physically correct, since in fact all gases ________________________ WORLD TECHNOLOGIES ________________________ turn into liquids at a low enough temperature, and Charles' law is not applicable at low temperatures for this reason. The fact that the gas will occupy a non-zero volume - even as the temperature approaches absolute zero - arises fundamentally from the uncertainty principle of quantum theory. However, as the temperature is reduced, gases turn into liquids long before the limits of the uncertainty principle come into play due to the attractive forces between molecules which are neglected by Charles' Law. Relation to the ideal gas law French physicist Émile Clapeyron combined Charles' law with Boyle's law in 1834 to produce a single statement which would become known as the ideal gas law. Cla-ypeyron's original statement was: where t is the Celsius temperature; and p 0 , V 0 and t 0 are the pressure, volume and temperature of a sample of gas under some standard state.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Chemistry

  With Inorganic Qualitative Analysis

  • Therald Moeller(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  Figure 3.10 . The dashed portion of the plot illustrates a “logical” conclusion from Charles’ observations: If a gas were cooled to -273.15°C, it would disappear entirely. This, of course, does not happen. Charles’ law becomes a less and less accurate description of gas behavior as the gas molecules get closer together. With decreasing volume, the force of attraction between molecules increases and the real volume of the molecules occupies a larger percentage of the total volume-that is, the gas becomes less ideal. Before

  FIGURE 3.10 Charles’ law.

  Volume is plotted versus temperature at constant pressure. This graph shows the variation in the volume of 1 mole of an ideal gas with changing temperature. The equivalent temperatures on the Celsius and Kelvin scales are shown. Note that when the temperature doubles(2 × 273°K) the volume occupied by 1 mole doubles.

  Charles’s law: At constant P, V is inversely proportional to T

  -273.15°C is reached, the gas molecules get close enough together for the force of attraction between them to overcome the energy of their random motion; as a result, the gas liquefies or solidifies.

  Absolute zero , -273.15°C, is the lowest possible temperature. It has been approached as closely as -273.148°C, but never attained. About 100 years after Charles formulated his law, the British physicist Lord Kelvin hit upon the idea of an absolute temperature scale -a scale that takes absolute zero as its zero point. The Kelvin scale (see Figure 1.3 ) is the absolute temperature scale based on the Celsius scale. (There are other absolute temperature scales; the only requirement is that on an absolute scale the zero point is absolute zero.) Kelvin’s scale simplified the statement of Charles’ law : At constant pressure, the volume of a given mass of gas is directly proportional to the absolute temperature . Mathematically, Charles’ law takes the following forms:

  At constant pressure,

  If the volume or temperature of a given mass of gas is changed at constant pressure, the following expression relates the initial to the final conditions:

  (5)

  EXAMPLE 3.2

  A cylinder with a movable piston is filled at 24°C with a gas that occupies 36.2 cm3 . If the maximum capacity of the cylinder is 65.2 cm3

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  A Mole of Chemistry

  An Historical and Conceptual Approach to Fundamental Ideas in Chemistry

  • Caroline Desgranges, Jerome Delhommelle(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  1 ! He finds the same formula for different gases such as oxygen, nitrogen and hydrogen. He names this relation Charles’ law in Charles’ honor. He also notes that, if he draws a graph for the volume against the temperature, a volume of gas of zero (V = 0) is reached for a temperature of –266.66°C! For Gay-Lussac, this shows that Charles’s law must be taken with caution and does not apply at low temperatures. Nevertheless, Lord Kelvin will give another meaning to this number representing the “infinite cold” or absolute zero, leading to an entirely new science, now known as thermodynamics!

  Gay-Lussac also uses the data for the different heights of mercury from his experiments. He deduces that the pressure of the gas increases when temperature increases. Repeating the same process as before, i.e. looking at two experiments for two different temperatures, he finds that P1 T2  = P2 T1 ! This law is called Gay-Lussac’s law. Gathering Boyle’s, Charles’ and Gay-Lussac’s laws, we obtain the famous combined gas law that gives the relationship between temperature, pressure and volume for any gas. Using mathematical equations, this translates into PV = constant (Boyle’s law), V/T = constant (Charles’ law) and P/T = constant (Gay-Lussac’s law). It thus follows that (PV)/T = constant… Q.E.D.! This is a very powerful formula that can be used to solve practical problems. For instance, consider a gas at temperature T1 , with volume V1 and pressure P1 . If we increase the temperature to twice the initial value (T2  = 2T1 ) and keep the same volume (V2  = V1 ), we can calculate the pressure P2  = (P1 V1 T2 )/(V2 T1 ). We thus find that, since V2  = V1 and T2  = 2T1 , P2  = 2P1 ! In other words, when a gas is enclosed in a vessel of fixed volume and we warm it up to twice the initial temperature, we find that the pressure at this new temperature is twice the value it had at the beginning of the experiment! We can also solve much more complex problems, for which two variables change, for instance, P and V, or P and T, or T and V. We just need to use the fact that (P1 V1 )/T1  = (P2 V2 )/T2

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Introductory Chemistry

  An Active Learning Approach

  • Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  The quantitative problem-solving methods you learned in Chapter 3 are used to convert from one pressure unit to another. Goal 10 When plotting the relationship between gas volume and temperature, explain how the straight line can be extrapolated to determine the temperature at which the gas has zero volume, and explain the significance of this temperature. Gas volume and absolute temperature are directly proportional for a fixed amount of gas at constant pressure. When the relationship is extrapolated to zero volume, the trend line reaches the temperature axis at 0 K, –273°C. This is absolute zero, the lowest temperature. Goal 11 Describe the relationship between the volume and temperature of a fixed amount of a gas at constant pressure, and express that relationship as a proportionality, an equality, and a graph. Charles’s Law states that the volume of a fixed quantity of gas at constant pres- sure is directly proportional to absolute temperature, V ~ T and V = kT. The plot of volume versus temperature is a straight line that passes through the origin. Goal 12 Given the initial volume (or temperature) and the initial and final temperatures (or vol- umes) of a fixed amount of gas at constant pres- sure, calculate the final volume (or temperature). For a fixed amount of gas at constant pressure, V 1 T 1 5 V 2 T 2 . Goal 13 Describe the relationship between the volume and pressure of a fixed amount of a gas at constant temperature, and express that rela- tionship as a proportionality, an equality, and a graph. Boyle’s Law states that for a fixed amount of gas at constant temperature, pressure is inversely proportional to volume, P ~ 1/V and P = k(1/V) or PV = k. The plot of pressure versus the inverse of volume is a straight line that passes through the origin. Goal 14 Given the initial volume (or pressure) and initial and final pressures (or volumes) of a fixed amount of gas at constant temperature, calculate the final volume (or pressure).

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  Fig. 6.10B , the pressure and temperature become directly proportional and pressure becomes equal to zero at 0 K.

  Fig. 6.10 The pressure of a gas sample as a function of temperature in degrees Celsius (A) and Kelvin (B).

  The modern statement of Gay-Lussac’s law is;

  •  At constant volume, the pressure of a fixed mass of any gas is directly proportional to the absolute temperature in degrees Kelvin.

  P = k T

    (9)

  This means that since the ratio of pressure to temperature for any gas at constant pressure is (P /T  = k ), if the pressure or temperature of the gas is changed, the effect on the other variable can be calculated by;

  P 1

  /

  T 1

  =

  P 2

  /

  T 2

    (10)

  Example 6.4: Determining the Pressure of a Gas After a Change in Temperature at Constant Volume and Mass If a gas contained in a steel tank at 21.4°C has a pressure of 5.17 atm. What will the pressure be if it is heated to a temperature of 89.6°C? According to Gay-Lussac’s Law:

  P 1

  = 5.17 atm ,

  T 1

  = 21 .

  4 °

  C = 21.4 + 273.15 = 294.6 K

  T 2

  = 37 .

  5 °

  C = 37.5 + 273.15 = 310.7 K

  So

  P 1

  /

  T 1

  =

  P 2

  /

  T 2

  P 2

  =

  P 1

  T 2

  /

  T 1

  =

  5.17 atm

  310.7 K

  294.6 K

  = 5.45 atm

  6.5 The Ideal Gas Law

  Boyle’s law, Charles’ law, and Gay-Lussac’s law each describe relationships between pairs of the three important variables that determine the behavior of a gas (temperature, pressure, and volume). In order to determine the values of all three variables when more than one is changing, the three gas laws can be combined into a single law. This gives a relationship between pressure, volume, and temperature for a fixed amount of any gas expressed as a single equation called the combined gas law

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Definitions, Conversions, and Calculations for Occupational Safety and Health Professionals

  • Edward W. Finucane(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  P 1 V 1 = P 2 V 2 Where: P 1 = the Pressure of a gas @ Time #1, measured in some suitable pressure units; V 1 = the Volume of that same gas @ Time #1, measured in some suitable volumetric units; P 2 = the Pressure of that same gas @ Time #2, measured in the same pressure units as P 1 above; & V 2 = the Volume of that same gas @ Time #2, measured in the same volumetric units as V 1 above Equation #1-6 : The following relationship, Equation #1-6 , is Charles' Law, which describes how the Vol-ume and the Absolute Temperature of a gas vary under conditions of constant pressure . V 1 T 1 = V 2 T 2 Where: V 1 & V 2 are the Volumes of the gas of interest at each of its two states, with this term as was defined for Equation #1-5 , above on this page; T 1 = the Absolute Temperature of a gas @ Time #1, measured in either K or ° R; & T 2 = the Absolute Temperature of the same gas @ Time #2, measured in the same Absolute Temperature units as T 1 DEFINITIONS, CONVERSIONS, AND CALCULATIONS 1-18 Equation #1-7 : The following relationship, Equation #1-7 , is Gay-Lussac's Law, which describes how the Pressure and Temperature of a gas vary under conditions of constant volume . P 1 T 1 = P 2 T 2 Where: P 1 & P 2 are the Pressures of the gas of interest at each of its two states, with this term as was defined for Equation #1-5 on the previous page, namely, Page 1-17; & T 1 & T 2 are the Absolute Temperatures of the gas of interest at each of its two states, with this term as was defined for Equation #1-6 , on the previous page, namely, Page 1-17. Equation #1-8 : The following formula, Equation # 1-8 , is the General Gas Law, which is the more general-ized relationship involving changes in any of the basic measurable characteristics of any gas.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Physical Chemistry

  • David Ball(Author)
  • 2014(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 6 Chapter 1 | Gases and the Zeroth Law of Thermodynamics Unless otherwise noted, all art on this page is © Cengage Learning 2014. where the function is written as F ( p, V ) to emphasize that the variables are pressure and volume, and that the outcome yields the value of the temperature T . Equations like equation 1.1 are called equations of state. One can also define equations of state that yield p or V instead of T . In fact, many equations of state can be algebraically rearranged to yield one of several possible state variables. The earliest equations of state for gases were determined by Boyle, Charles, Amontons, Avogadro, Gay-Lussac, and others. We know these equations as the various gas laws. In the case of Boyle’s gas law, the equation of state involves multiplying the pressure by the volume to get a number whose value depended on the temperature of the gas: p # V 5 F 1 T 2 at fixed n (1.2) whereas Charles’s gas law involves volume and temperature: V T 5 F 1 p 2 at fixed n (1.3) Avogadro’s law relates volume and amount, but at fixed temperature and pressure: V 5 F 1 n 2 at fixed T, p (1.4) In the above three equations, if the temperature, pressure, or amount were kept constant, then the respective functions F ( T ) , F ( p ) , and F ( n ) would be constants. This means that if one of the state variables that can change does, the other must also change in order for the gas law to yield the same constant.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  College Physics

  • Paul Peter Urone, Roger Hinrichs(Authors)
  • 2012(Publication Date)
  • Openstax

    (Publisher)

  In contrast, in liquids and solids, atoms and molecules are closer together and are quite sensitive to the forces between them. Figure 13.17 Atoms and molecules in a gas are typically widely separated, as shown. Because the forces between them are quite weak at these distances, the properties of a gas depend more on the number of atoms per unit volume and on temperature than on the type of atom. To get some idea of how pressure, temperature, and volume of a gas are related to one another, consider what happens when you pump air into an initially deflated tire. The tire’s volume first increases in direct proportion to the amount of air injected, without much increase in the tire pressure. Once the tire has expanded to nearly its full size, the walls limit volume expansion. If we continue to pump air into it, the pressure increases. The pressure will further increase when the car is driven and the tires move. Most manufacturers specify optimal tire pressure for cold tires. (See Figure 13.18.) Chapter 13 | Temperature, Kinetic Theory, and the Gas Laws 485 Figure 13.18 (a) When air is pumped into a deflated tire, its volume first increases without much increase in pressure. (b) When the tire is filled to a certain point, the tire walls resist further expansion and the pressure increases with more air. (c) Once the tire is inflated, its pressure increases with temperature. At room temperatures, collisions between atoms and molecules can be ignored. In this case, the gas is called an ideal gas, in which case the relationship between the pressure, volume, and temperature is given by the equation of state called the ideal gas law. Ideal Gas Law The ideal gas law states that (13.18) PV = NkT , where P is the absolute pressure of a gas, V is the volume it occupies, N is the number of atoms and molecules in the gas, and T is its absolute temperature.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Chemistry

  An Atoms First Approach

  • Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  FIGURE 8.15 The effects of decreasing the volume of a sample of gas at constant temperature. a b c ▲ (a) A balloon filled with air at room temperature. (b) Liquid nitrogen at 77 K is poured onto the balloon. (c) The balloon collapses as the molecules inside slow down due to the decreased temperature. Slower molecules produce a lower pressure. Chip Clark/Fundamental Photographs Chip Clark/Fundamental Photographs Chip Clark/Fundamental Photographs 342 CHAPTER 8 Gases Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. The KMT accounts for this behavior because when the temperature of a gas increases, the speeds of its particles increase; the particles hit the wall with greater force and greater frequency. Since the volume remains the same, this would result in increased gas pressure, as illustrated in Fig. 8.16. CRITICAL THINKING You have learned the postulates of the KMT. What if we could not assume the third postulate to be true? How would this affect the measured pressure of a gas? Volume and Temperature (Charles’s Law) The ideal gas law indicates that for a given sample of gas at a constant pressure, the volume of the gas is directly proportional to the temperature in kelvins: V 5 S nR P D T h Constant This can be visualized from the KMT, as shown in Fig. 8.17. When the gas is heated to a higher temperature, the speeds of its molecules increase and thus they hit the walls more often and with more force. The only way to keep the pressure constant in this situation is to increase the volume of the container.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  pressure is produced by molecular collisions on the walls of the container; pressure increases with increasing energy of collisions and increasing number of collisions. Pressure is affected by the following variables.

  (1)  Pressure is proportional to the energy of molecular collisions (kE(average) ): P ∝ kE(average) . Since kE(average) ∝ RT, and this produces the relationship: P ∝ RT. Charles’s law states that the pressure of a gas is directly proportional to temperature.

  (2)  Pressure is proportional to the number of collisions per time. As the volume of a container decreases, the number of collisions with the container walls increases; pressure is inversely proportional to the volume (Boyle’s law): P ∝ 1/V

  (3)  The number of collisions increases as the number of molecules in a container increases; pressure is proportional to the number of moles (symbol = n) of gas in a container: P ∝ n

  Combining all variables: P ∝ (n) × (RT) × (1/V) or P ∝ nRT/V

  The constant (R) when expressed in the correct units is the only constant required; the equation produced is

  P = nRT/V or PV = nRT

  The units of volume are liters (L); the pressure is measured in atmospheres (atm); the temperature must be in Kelvin (K). The molar gas constant (R) has a different value for the different units of this equation. The units of R must be derived from the other variables:

  R =

  PV nT

  =

  atmospheres  ×  liters

  moles  ×  Kelvin

  ;   R =  0.0821   Liter-atm   /   mole-K

  MEASUREMENTS OF GAS PRESSURE

  Pressure is measured as a force per unit area. In the metric system, force is measured in units of kg-m/sec2 and area is in square meters (m2 ). Force per (i.e., divided by) area is:

  kg-m /

  sec 2

  m 2

  . The resulting unit is kg/m-sec2 and is defined as the Pascal (Pa).

  In this English system, force per unit area is stated as pounds per square inch (psi). Pressure can be measured by a manometer or barometer. Gas pressure is indicated by the height of a column of a liquid that can be supported by the pressure of the gas. The average pressure of the atmosphere at sea level will support a column of mercury liquid to a height of 760 millimeters (mm). This specific pressure, termed 760 mmHg (or 760 torr), is standardized as equal to one atmosphere (atm

  Sign up to read

  Learn more about book