Charless Law

The effect of temperature on the volume of a gas was observed in about 1787 by the French physicist J. A. C. Charles (1746-1823). Charles found that various gases expanded by the same fractional amount when they underwent the same change in temperature. Later it was found that if a given volume of any gas initially at 0°C was cooled by 1°C, the volume decreased by if cooled by 2 C, it decreased by if cooled by 20°C, by and so on. Since each degree of cooling reduced the volume by, it was apparent that any quantity of any gas would have zero volume if it could be cooled to —273°C. Of course, no real gas can be cooled to —273°C for the simple reason that it would liquefy before that temperature is reached. However, —273°C (more precisely, -273.15°C) is referred to as absolute zero this temperature is the zero point on the Kelvin (absolute) temperature scale— the temperature at which the volume of an ideal, or perfect, gas would become zero. 

Volume-temperature relationship of methane (CH4). Extrapolated portion of the graph is shown by the broken line. 

At constant pressure the volume of a fixed mass of any gas is directly proportional to the absolute temperature, which may be expressed as 

Mathematically, this states that the volume of a gas varies directly with the absolute A capital TIs usually used temperature when the pressure remains constant. In equation form, Charles law may for absolute temperature (K) be written as and a small f for °C. 

Another equation relating the volume of a gas at two different temperatures is 

If a given quantity of gas is heated at constant pressure in a container that has a movable wall, such as a piston (Fig. 12-4), the volume of the gas will increase. If a given quantity of gas is heated in a container that has a fixed volume (Fig. 12-5), its pressure will increase. Conversely, cooling a gas at constant pressure causes a decrease in its volume, while cooling it at constant volume causes a decrease in its pressure. 

Charles (1746-1823) observed, and J. L. Gay-Lussac (1778-1850) confirmed, that when a given sample of gas is cooled at constant pressure, it shrinks by times its volume at 0°C for every degree Celsius that it is cooled. Conversely, when the sample of gas is heated at constant pressure, it expands by times its volume at 0°C for every degree Celsius that it is heated. The changes in volume with temperature of two different-sized samples of a gas are shown in Fig. 12-6. 

The chemical identity of the gas has no influence on the volume changes as long as the gas does not liquefy in the range of temperatures studied. It is seen in Fig. 12-6 that for each sample, the volume of the 

In Fig. 12-6, the volume can be seen to be directly proportional to the Kelvin temperature, since the lines go through the zero-volume point at 0 K. 

EXAMPLE 12.6. What are the freezing point of water and the normal boiling point of water on the Kelvin scale Ans. Freezing point of water = 0°C -F 273° = 273 K 

The fact that gas volumes change when the temperature changes can also be treated mathematically. In this case, it is a direct relationship rather than an inverse one. As temperature increases, the volume increases. And as temperature decreases, the volume decreases. This means that if we were to divide the volume by the temperature we would obtain a constant. 

FIGURE 9.8 Heating the piston-cylinder arrangement causes the temperature to increase from T, to T2 and the volume to increeise from V, to Vj. (From Kenkel, J., Kelter, P., and Hage, D., Chemistry An Industry-Based Introduction with CD-ROM, CRC Press, Boca Raton, FL, 2001. With Permission.) 

From this observation, we can obtain the following relationship  

A gas occupies a volume of 5.28 L at a temperature of 31°C. What volume will this gas occupy if the temperature is changed to 61°C while the pressure is held constant  

Charles law applies because the temperature is changing at constant pressure. Solving Equation 9.8 for Vj, we get the following  

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Charles law, also known as Gay-Lussac s law, states that the volume of a given mass of gas varies directly as the absolute temperature if the pressure remains constant, that is. 

Characteristic curves. 3 Charles Law, 15 Check valves, 472 Chord, 226 Clearance... 

Tlie two precursors of tlie ideal gas law were Boyle s low and Charles law. Boyle found tliat tlie volume of a given mass of gas is inversely proportional to die absolute pressure if die temperature is kept constant, tliat is,... 

The ideal gas law or perfect gas law is a combination of Boyle s and Charles laws for any compressible fluid (gas/vapor). 

Q = volume flow of gas, fF/min at inlet conditions Charles Law at Constant Pressure ... 

From combined Boyle s and Charles Law Equation of State for Perfect Gas ... 

Ideal (or perfect) gas behavior is approached by most vapors and gases in the limit of low pressures and elevated temperatures. Two special forms of restricted utility known as the Boyle s law and the Charles law preceded the development of the perfect gas law. 

Pressure, temperature, and volume are properties of gases that are completely interrelated. Boyle s law and Charles law may be combined into one equation that is referred to as the ideal gas law. This equation is always true for ideal gases and is true for real gases under certain conditions. 

As oil is pumped into the accumulator, compressing the nitrogen, the nitrogen temperature increases (Charles law). Therefore, the amount of oil stored will not be quite as much as calculated with Boyle s law unless sufficient time is allowed for the accumulator to cool to atmospheric temperature. Likewise, when oil is discharged, the expanding nitrogen is cooled. So, the discharge volume... 

If a fixed quantity of gas is held at a constant pressure and heated or cooled, its volume will change. According to Charles law, the volume of a gas at constant pressure is directly proportional to the absolute temperature. This is shown by the following equation ... 

Basic concepts discussed here are atmospheric pressure vacuum gage pressure absolute pressure Boyle s law or pressure/volume relationship Charles law or temper-ature/volume relationship combined effects of pressure, temperature and volume and generation of pressure or compression. 

Charles Law states that, for an ideal gas, the volume at constant pressure is proportional to the absolute temperature ... 

Boyle s and Charles laws can he combined into the ideal gas equation ... 

This direct relation between volume and temperature (at constant pressure) is called Charles Law. 

Charles, Jacques, 57 Charles law, 58 Chemical bonding, see Bonding Chemical bonds, see Bond Chemical change, 38 Chemical energy, 119 Chemical equations, see Equations Chemical equilibrium, law of, 152 Chemical formulas, see Formula Chemical kinetics, 124 Chemical reactions, see Reactions Chemical stability, 30 Chemical symbols, 30 not from common names, 31 see inside back cover Chemotherapy, 434 Chlorate ion, 360 Chloric acid, 359 Chlorides chemistry of, 99 of alkali metals, 93,103 of third-row elements, 103 Chlorine... 

The fact that the volume of a gas varies linearly with temperature is combined with the concept of absolute temperature to give a statement of Charles law ... 

It would be equally correct to consider that first the temperature of the gas was changed from T, to 7 at the constant pressure P, for which a new volume Fj, could be calculated using Charles law. Then, assuming that the temperature is held constant at 7, calculate how the volume would change as the pressure is changed from 7, to P2 (Fig. 11-9). 

Using the reciprocal of the equation usually used for Charles law ... 

Which temperature scale must be used in (a) Charles law problems (h) ideal gas law problems (e) combined gas law problems (<7) Boyle s law problems ... 

Ans. (a) The ratio is smaller at 400 K. The volume of the molecules themselves would not change appreciably between the two temperatures, but the gas volume changes according to Charles law. (b) Since the gas volume is larger at 400K, the gas molecules are farther apart at that temperature, and exhibit lower intermolccular forces. The gas would therefore be more ideal at the higher temperature. 

Charles law for a given sample of gas at constant pressure, the volume is directly proportional to the absolute temperature V=kT. 

The quantitative relationship of gas volume and temperature is stated in Charles Law ... 

Charles Law. John L. Park, 1996, http //dbhs.wvusd.k12.ca.us/GasLaw/Gas-Charles.html... 

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