Laws of perfect gas

Intro:-                                                     

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 please called vapour. A vapour contains some particles of liquid in suspension. The behaviour of superheated vapour 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
3) temperature of the gas

The behaviour of a perfect gas undergoing in change in these three variables is governed by the following laws

Boyle’s law:- this law was formulated by Robert boyle in 1662. It state that ” the absolute pressure of a given mass of a perfect gas various inversely as its volume when the temperature remains constant ”

Expression,

p α 1 / v  or, pv = constant

the more useful from of the above equations is,

 

p1v1 = p2v2 = p3v3 =…. = constant

Charles law:- who was formulated by a Frenchman Jacques A.C Charles in about 1787. It may be stated in two different forms

Expression,

v α T    or,  v / T = constant

or,    v1 / T1 = v2 / T2 = v3 / T3 = constant

i) the volume of a mass of perfect gas barriers directly as it Absolute Temperature when the absolute pressure remains constant.
ii) All perfect gases change in volume 1 / 273 th of its original volume at 0°C for 1°C change in temperature when the pressure remain constant.
Let, v0 = volume of a given mass of gas at 0°C.
vt = volume of the same mass of gases at t°C.

then, according to the above statement,

vt = v0 + 1 / 273 v0 t = v0 (273 + t / 273) = v0 x T / T0

vt  / T = v0 / T0

T = Absolute temp. corresponding to t0 C.

T0 = Absolute temp. corresponding to 0o C.

Gay lussac law:-  this lost states ” the absolute pressure of a given mass of a perfect gas varies directly as it Absolute Temperature, when the volume remains constant.

Expression

p α T      or   p / T = constant.

P1 / T1 = p2 / T2 = p3 / T3 = ……. = constant.

 

General gas equation:- The gas laws as discused the relation b/w the two variables when the third variable is constant. But in actual practice, all the three variables i.e… pressure, volume and tempreature, change simultaneously. In order to deal with all practical cases, the Boyle’s law and Charles’s law are combined toghter, which give us a general gas equation.

According to Boyle’s law

pα 1 / v      or     v α 1 / p       (T = constant)

 And according to Charles’s

v α T                     (p = constant)

It is obvious that

v α 1 / p  and T both          or   v α T / p

pv  α T          or  pv = CT

where C is constant, whose value depends

 upon the mass and properties of the gas concerned.

The more useful from of the general gas equation is,,,…

 p 1 v1 / T1 = p2 v2 / T2 = p3 v3 / T3 = ….. = constant .

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