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3.10.3 Expansion in gases
A gradual expansion without change in temperature is termed isothermal. 
A gradual expansion without transfer of heat to or from the gas is termed 
adiabatic.
If the temperature of a fixed mass of a gas was held constant while its 
volume was varied over wide limits, then the pressure exerted by the gas 
varies also in such a way that the product of pressure and volume remained 
approximately constant. This relation is known as Boyle's law may be 
written in the form:
P * V = constant (18)
Fig.8. show the relation between the volume and pressure of the gas at 
constant temperature.
Fig.8. Expansion of gases under constant temperature
All gases tend to expand when heated, and if the gas is allowed to expand 
by a suitable amount, then the pressure may be kept constant. Charles’s 
constant pressure law states that at constant pressure, for a rise in
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temperature, all gases expand by a constant amount, equal to about 1/273 
the law states that:
Vt = Vo (1 + α t) (19)
Where Vt is the volume at t oC,
Vo is the volume at 0 oC and
α is the temperature coefficient of increase of volume at constant pressure.
(α = 1/273 approximately).
Fig.9. show the thermal expansion of gas at constant pressure.
Fig. 9. Expansion of gas under thermal pressure
If the volume of the gas is kept constant, then the pressure increases with 
temperature according to the relation:
Pt = Po (1 + β t) (20)
Where Pt is the pressure at t oC,
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temperature, all gases expand by a constant amount, equal to about 1/273 
the law states that:
Vt = Vo (1 + α t) (19)
Where Vt is the volume at t oC,
Vo is the volume at 0 oC and
α is the temperature coefficient of increase of volume at constant pressure.
(α = 1/273 approximately).
Fig.9. show the thermal expansion of gas at constant pressure.
Fig. 9. Expansion of gas under thermal pressure
If the volume of the gas is kept constant, then the pressure increases with 
temperature according to the relation:
Pt = Po (1 + β t) (20)
Where Pt is the pressure at t oC,