Gas Laws:
In this topic, we shall get to understand that the three properties of a gas that are necessary to describe the state of gas are pressure, temperature and volume of the gas. For a given mass of gas, the three properties are related by the gas laws.
The properties are volume, pressure and temperature.
Gas Pressure and Measurement of gas pressure:
Gas Pressure:
Gas pressure is the force per unit area that is exerted by a gas.
Manometer:
Manometer is the instrument that is used to measure gas pressure.
Construction of Manometer:
A manometer is a U – tube which contain either water or mercury. One end of the open tube is connected to a gas supply while the other end is open to the atmosphere.
Manometer for Measuring Gass Pressure:
Operations of Manometer:
With the gas supply off, the arms of the U – tube is adjusted so that the water or mercury levels are the same in both arms of the tube. When the gas supply is opened, the gas exert a pressure at point A. This pressure causes the water or mercury level in the open arm of the tube at point B to rise to a particular height h, above point B.
Formula for calculation:
Since points A and point B are at the same level in both arms of the tube, we will use the theory,
pressure at point A = pressure at point C
Pressure at point A is the gas pressure that is being supplied to the left arm of the manometer while pressure at point C is the pressure due the height of water or mercury column.
Therefore, for water used in the manometer,
pressure at point B =
= Pressure due water height h + atmospheric pressure
Pressure point B
= height of water*density of water*acceleration due to gravity + atm. Pressure
Pressure at point B = h*qw*g + atmospheric pressure(760mmHg)
Let us equate the two pressures.
The formula will be:
Pressure at point A = pressure at point B
Gas pressure at point A = pressure due to water column of height h
Gas pressure at point A = hw * qw * g + atmp pressure.(760mmHg)
At this point, you make the variable that you want to calculate subject of the formula.
Note:
Hw is height of water column of height h.
qw is density of water.
g is acceleration due to gravity. ( g = 9.8m/s²)
While for mercury,
Pressure at point B =
= height of mercury*density*acce due to gravity + atmp pressure (76ommHg)
Pressure at point B = hm * qm * g + atmp pressure(760mmHg)
Therefore,
The formula will be:
Gas pressure at point A = hm * qm * g + atmp pressure.(760mmHg)
At this point, you make the variable that you want to calculate subject of the formula.
Note:
Hm is height of mercury column.
qm is density of mercury.
g is acceleration due to gravity. ( g = 9.8m/s²)
Worked Examples:
I. Calculate the pressure of gas that will raise water to a height of 26cm in a monometer. ( atmp pressure = 76cm hg, qw = 1 g/cm³, g = 9.8 m/s² )
Solution:
Data given in the question:
Height of water column h = 26cm, g = 9.8m/s, atmp pressure = 76cm hg,
qw = 1 g/cm³.
Formula:
gas pressure at A = pressure at B due to height of water + atmp pressure(76cmHg)
. gas pressure = qw * hw * g + atmp pressure
Substitution:
gas pressure = 1* 26 * 9.8 + 76.
Gas pressure = 254.8 + 76 = 330.8 N/m²
II. Calculate the height of mercury Column the a gas pressure of 352 N/m² will sustain in a manometer whose arm is opened. ( p = 76 cm Hg, g = 10m/s² ).
Solution:
Data given in the question:
Gas pressure = 3.52x105N/m², atmp = 76cm = 0.76m Hg, g = 10 m/s², qm = 1300kg/m³
Pressure due to 76cm Hg = hpg = 0.76*1300*9.8 = 101293 N/m²
Diagram here:
Theory of calculation:
Gas pressure at point A = pressure at B due to mercury height h
Formula:
gas pressure at A = hm * pm * g + atmp pressure.
Substitution:
3.25x105 = 13000*h*9.8 + 101293
3.25x105 = 12740*h + 101293
Collect like terms:
325000 – 101293 = 12740*h
224707 = 12740*h
Make h the subject:
224707 ÷ 12740 = h. ➡ h = 17.64 m
We can obtain an important formula by equating pressure due to water height to that of mercury.
Therefore,
Pressure due to height of water = pressure due to height of mercury
Pressure due to height of water = hw*qw*g
Pressure due to height of mercury = hm*qm *g
Therefore,
Hw * Qw * g = Hm * Qm * g (g cancels g )
Therefore,
Hw * Qw = Hm * Qm
Make
In this topic, we shall get to understand that the three properties of a gas that are necessary to describe the state of gas are pressure, temperature and volume of the gas. For a given mass of gas, the three properties are related by the gas laws.
The properties are volume, pressure and temperature.
Gas Pressure and Measurement of gas pressure:
Gas Pressure:
Gas pressure is the force per unit area that is exerted by a gas.
Manometer:
Manometer is the instrument that is used to measure gas pressure.
Construction of Manometer:
A manometer is a U – tube which contain either water or mercury. One end of the open tube is connected to a gas supply while the other end is open to the atmosphere.
Manometer for Measuring Gass Pressure:
Operations of Manometer:
With the gas supply off, the arms of the U – tube is adjusted so that the water or mercury levels are the same in both arms of the tube. When the gas supply is opened, the gas exert a pressure at point A. This pressure causes the water or mercury level in the open arm of the tube at point B to rise to a particular height h, above point B.
Formula for calculation:
Since points A and point B are at the same level in both arms of the tube, we will use the theory,
pressure at point A = pressure at point C
Pressure at point A is the gas pressure that is being supplied to the left arm of the manometer while pressure at point C is the pressure due the height of water or mercury column.
Therefore, for water used in the manometer,
pressure at point B =
= Pressure due water height h + atmospheric pressure
Pressure point B
= height of water*density of water*acceleration due to gravity + atm. Pressure
Pressure at point B = h*qw*g + atmospheric pressure(760mmHg)
Let us equate the two pressures.
The formula will be:
Pressure at point A = pressure at point B
Gas pressure at point A = pressure due to water column of height h
Gas pressure at point A = hw * qw * g + atmp pressure.(760mmHg)
At this point, you make the variable that you want to calculate subject of the formula.
Note:
Hw is height of water column of height h.
qw is density of water.
g is acceleration due to gravity. ( g = 9.8m/s²)
While for mercury,
Pressure at point B =
= height of mercury*density*acce due to gravity + atmp pressure (76ommHg)
Pressure at point B = hm * qm * g + atmp pressure(760mmHg)
Therefore,
The formula will be:
Gas pressure at point A = hm * qm * g + atmp pressure.(760mmHg)
At this point, you make the variable that you want to calculate subject of the formula.
Note:
Hm is height of mercury column.
qm is density of mercury.
g is acceleration due to gravity. ( g = 9.8m/s²)
Worked Examples:
I. Calculate the pressure of gas that will raise water to a height of 26cm in a monometer. ( atmp pressure = 76cm hg, qw = 1 g/cm³, g = 9.8 m/s² )
Solution:
Data given in the question:
Height of water column h = 26cm, g = 9.8m/s, atmp pressure = 76cm hg,
qw = 1 g/cm³.
Formula:
gas pressure at A = pressure at B due to height of water + atmp pressure(76cmHg)
. gas pressure = qw * hw * g + atmp pressure
Substitution:
gas pressure = 1* 26 * 9.8 + 76.
Gas pressure = 254.8 + 76 = 330.8 N/m²
II. Calculate the height of mercury Column the a gas pressure of 352 N/m² will sustain in a manometer whose arm is opened. ( p = 76 cm Hg, g = 10m/s² ).
Solution:
Data given in the question:
Gas pressure = 3.52x105N/m², atmp = 76cm = 0.76m Hg, g = 10 m/s², qm = 1300kg/m³
Pressure due to 76cm Hg = hpg = 0.76*1300*9.8 = 101293 N/m²
Diagram here:
Theory of calculation:
Gas pressure at point A = pressure at B due to mercury height h
Formula:
gas pressure at A = hm * pm * g + atmp pressure.
Substitution:
3.25x105 = 13000*h*9.8 + 101293
3.25x105 = 12740*h + 101293
Collect like terms:
325000 – 101293 = 12740*h
224707 = 12740*h
Make h the subject:
224707 ÷ 12740 = h. ➡ h = 17.64 m
We can obtain an important formula by equating pressure due to water height to that of mercury.
Therefore,
Pressure due to height of water = pressure due to height of mercury
Pressure due to height of water = hw*qw*g
Pressure due to height of mercury = hm*qm *g
Therefore,
Hw * Qw * g = Hm * Qm * g (g cancels g )
Therefore,
Hw * Qw = Hm * Qm
Make
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