A perfect gas (or an ideal gas) may be defined as a state of a substance, whose evaporation from its liquid state is complete. It may be noted that if its evaporation is partial, the substance is called vapor. A vapor contains some particles of liquid in suspension. The behavior of super-heated vapors is similar to that of a perfect gas.
The physical properties of a gas are controlled by the following three variables :
1. Pressure exerted by the gas,
2. Volume occupied by the gas, and
3. Temperature of the gas.
The behavior of a perfect gas, undergoing any change in these three variables, is governed by the following laws :
1. Boyles law. This law was formulated by Robert Boyle in 1662. It states, "The absolute pressure of a given mass of a perfect gas varies inversely as its volume, when the temperature remains constant." Mathematically,
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Dswb2bX3+9/NbNi3UHdv/tg/8oKVnyr//+Lwfr9qxc+fmqkuWD/c//+pf3NpeuHh8bXrbk72Wl3/728jGZbojq7wgGhRIaITrWDc2iVJrpQkgVGak4ZfG2TGrDB9LIfAhtFk+PC8WkYlIHTOSUZoznpA4UMDcAoXqmLcna15EMuqbSPXCZlxTGBUypOeP+6ZYTZaWrJiaGvWBWI0cjCUL3EROiF2Rt8dMe+6FTC3WNhAZJZ09k5EnUuAyUFkSmlTZb3JeKS8WVFqTTPstpkEL6FBkI5Qc8K1UgFSPpjPq1JBsZ6f/t5WMq4NGuFAhAwNBILd8RwrhfCu2xS+Te5lVACtUjbIpG1eqR0YHe3gdeMOsFs6OZ/pHRPi49jTwVQ7oVnOhg0mi3IBfj94YQxoDUgh7J5Wbudl+7f//66Egflx4aCUZw6Vn1taUAUjt0jh6tJ06S4zi2soVZQM24TzJHV5KGPMVJg8kIS80D7nlBlsuAi4AuChUwkRPSJ2ukUSjgEqUEwWTAFROKS81z/hytQGqjUWrUGBoFWoF2ITRvGhiVrZPT4FTR2YRoCj1oC2lU425va1q58vORkVdz2YmmU/WtPzZ4wWzKkNpH3J8pVUsgj5MztP471k731QACQGgQGgQazbmvQUW0GDShMcYAAiKgQQCFiBj/1KAAqUSHJjR0BRFovgmN1irqAzIQxQHx2aptk4xiEM21FhokgGRBTiqmtQDUiEppobVEdCpERmsQcQwoAYEGGqSNUVGGmnNsRPoHPm6+H483tj9Z69T79MEXX3zU1/croOi5f6Ol+WjAslIHFhvXgrl1llS1xTmhTAfP6HSf2vkpA8O5r5SMdmgboky6ZJWqIydE5dWX3YpaHATMa2+xAucWSBEVFcaoyOm8MV2Zy6/xFtzYn4HQxn4LQGhNotJiNDNYunHVgwc3Ap79qe2H212XpArytXDhJM+FsGCZeB7GedMQlRBBQQhTOL2VCfkQGscY5JcaUrXT0OmZc95oFihqp+a/K4QFicH5h40LayGZb3IG1VXl16+137lzpa31ZC43BSiU/sMQWr4UgDCfcbH4W94hKmMwRV0+me+CYjwtL6V+227j74V49m4Q5u+wAIT5TyZ2piBP8+c7B80UCxyuryopWXK5s3VmdozaA8CItwKWGsnpUv5BmtOSmpyGF4iWCwncu9mr1C3qI00dROTjh4WOrt4gEvnVlcIQpj5v1MKC/x6Qb9Nin18YwshFoT5cX9XWepJSQzRSI/8/gZDKlQCuVUCr0H8UQtvCuzCE9mcYB1b/vyAEAK0VQWijzSguzYOQ8uj4rhMIJC4BNWow2gvmuPDIBVJvjgnfbjZToWk+hMYoQOqHSDqXoqxAMupjSJ232ZH0XSbbJjJcu5JMRkSM43NEOm2V9iQhH0LMa+otuI1YqgpCCFEvi7MNRwqji4ucbaY0ycD8phIs/I4k1qLDLa0FmqgfXCNQHupWv1KNYvn/U2EjbDqvsOlawhcjIW7T0sgVMAXcpsD0CvtI6gTqXbyv61BtYEwHI6TuCoRU3KaSrtWxZ6W2w8jNawtuJnUdkt4GASgBBfU0gZFgZP78RbbynW8xLAuoUdWF0HXjVCPNjA7e6bqSnZsiCMEghoZLrkALJTTOa9Vyy9mUFyfctMUX6shzG7YSsqVGLnVA+EkdSM1sD7V1ivkQuhFjqj8sxVz7rC3rJ518toaXkjynhc51yfmOYGGhsZ2iGEouvJw/rTQDIzCMS8oGhExqW/8LgFjEwcYvkd4AAAAASUVORK5CYII=)
The more useful form of the above equation is :
p1v1 = p2v2 = p3v3 = .. = Constant
where suffixes 1, 2 and 3 refer to different sets of conditions.
2. Charles' law. This law was formulated by a Frenchman Jacques A.C. Charles in about 1787. It may be stated in two different forms :
(i) "The volume of a given mass of a perfect gas varies directly as its absolute temperature, when the absolute pressure remains constant." Mathematically,
![](data:image/png;base64,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)
where suffixes 1, 2 and 3 refer to different sets of conditions.
(ii) "All perfect gases change in volume by 1 / 273 th of its original volume at 0° C for every 1° C change in temperature, when the pressure remains constant."
Let
Vo = Volume of a given mass of gas at 0° C, and
Vt = Volume of the same mass of gas at t° C.
Then, according to the above statement,
![](data:image/png;base64,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)
where
T = Absolute temperature corresponding to t° C.
To = Absolute temperature corresponding to 0° C.
A little consideration will show, that the volume of a gas goes on decreasing by 1/ 273th of its original volume for every 1°C decrease in temperature. It is thus obvious, that at a temperature of — 273° C, the volume of the gas would become zero. The temperature at which the volume of a gas becomes zero is called absolute zero temperature.
3. Gay Lussac law. This law states, "The absolute pressure of a given mass of a perfect gas varies directly as its absolute temperature, when the volume remains constant." Mathematically
![](data:image/png;base64,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)
where suffixes 1, 2 and 3.... refer to different sets of conditions.
Note : In dealing with a perfect gas, the values of pressure and temperature are expressed in absolute units.
The physical properties of a gas are controlled by the following three variables :
1. Pressure exerted by the gas,
2. Volume occupied by the gas, and
3. Temperature of the gas.
The behavior of a perfect gas, undergoing any change in these three variables, is governed by the following laws :
1. Boyles law. This law was formulated by Robert Boyle in 1662. It states, "The absolute pressure of a given mass of a perfect gas varies inversely as its volume, when the temperature remains constant." Mathematically,
The more useful form of the above equation is :
p1v1 = p2v2 = p3v3 = .. = Constant
where suffixes 1, 2 and 3 refer to different sets of conditions.
2. Charles' law. This law was formulated by a Frenchman Jacques A.C. Charles in about 1787. It may be stated in two different forms :
(i) "The volume of a given mass of a perfect gas varies directly as its absolute temperature, when the absolute pressure remains constant." Mathematically,
where suffixes 1, 2 and 3 refer to different sets of conditions.
(ii) "All perfect gases change in volume by 1 / 273 th of its original volume at 0° C for every 1° C change in temperature, when the pressure remains constant."
Let
Vo = Volume of a given mass of gas at 0° C, and
Vt = Volume of the same mass of gas at t° C.
Then, according to the above statement,
where
T = Absolute temperature corresponding to t° C.
To = Absolute temperature corresponding to 0° C.
A little consideration will show, that the volume of a gas goes on decreasing by 1/ 273th of its original volume for every 1°C decrease in temperature. It is thus obvious, that at a temperature of — 273° C, the volume of the gas would become zero. The temperature at which the volume of a gas becomes zero is called absolute zero temperature.
3. Gay Lussac law. This law states, "The absolute pressure of a given mass of a perfect gas varies directly as its absolute temperature, when the volume remains constant." Mathematically
where suffixes 1, 2 and 3.... refer to different sets of conditions.
Note : In dealing with a perfect gas, the values of pressure and temperature are expressed in absolute units.
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