The pressure-density relationship can be derived from the Boyle's law as shown below.
P₁V₁ = P₂V₂ (Boyle's law)
\({ P }_{ 1 }\frac { m }{ { d }_{ 1 } } ={ P }_{ 2 }\frac { m }{ { d }_{ 2 } } \)
where "m" is the mass, d ₁ and d₂ are the densities of gases at pressure P₁ and P₂ .
\(\frac { { P }_{ 1 } }{ { d }_{ 1 } } =\frac { { P }_{ 2 } }{ { d }_{ 2 } } \)
In other words, the density of a gas is directly proportional to pressure.

Gases which obey Boyle's Law and Charle's law or ideal gas equation PV = nRT are called ideal gases.
All gases whose behaviour is consistent with the assumption of kinetic theory of gases under all condition are called ideal gases.

Charles law states that "At constant pressure, the volume of a given mass of an ideal gas is directly proportional to its temperature." According to Charles Law, if we were to take a balloon filled with air and increase the temperature of the air inside, the volume of air would increase causing the balloon to expand. This is caused by the heating of the molecules of air inside the balloon causing them to move rapidly. In the same manner if we cooled the balloon in a freezer, the volume of air decreases, making the balloon look partially deflated.

At a given temperature the volume occupied by a fixed mass of a gas is inversely proportional to its pressure.
\(V\alpha \frac { 1 }{ P }\) at constant T& n.
Mathematical form: P₁V₁ = P₂ V₂ = K

The temperature below which a gas obeys Joule - Thomson effect is called inversion temperature (T_i). This value is given using van der waals constants a and b.,
\(T_i=\frac{2a}{Rb}\)

The pressure decreases with the increase in altitude because there are fewer molecules per unit volume of air. Above 9200 m (30,000 ft), for example, where most commercial aeroplanes fly, the pressure is so low that one could pass out for lack of oxygen. For this reason most aeroplanes cabins are artificially pressurized.

(i) The pressure exerted on a unit area of Earth by the column of air above it is called atmospheric pressure.
(ii) The standard atmospheric pressure = 1 atm.
(iii) 1 atm = 760 mm Hg.

At constant volume the pressure of a fixed mass of a gas is directly proportional to temperature, P ∝ T
or \(\frac{P}{T}\) = Constant k
If P₁ and P₂ are the pressures at temperatures T₁ and T₂ respectively, then from Gay Lussac's law
\(\frac { { P }_{ 1 } }{ { T }_{ 1 } } =\frac { { P }_{ 2 } }{ { T }_{ 2 } } \)

Given data P₁ = 1.2 atm
T₁ = 18° C
T₁ = 18 + 273 = 291 K
P₂ = ?
T₂ = 85° C
= 85 + 273 = 358 K
\(\frac { { P }_{ 1 } }{ { T }_{ 1 } } =\frac { { P }_{ 2 } }{ { T }_{ 2 } } \)
\({ P }_{ 2 }=\frac { { P }_{ 1 }{ T }_{ 2 } }{ { T }_{ 1 } } =\frac { 1.2\times 358 }{ 291 } \)
P₂ = 1.48 atm

Pressure in each compartment is same, p.
Temperature will remain same, t °C.
Density will remain same, d gcm^-3.
The number of moles in each component will be, \(\frac { n }{ 4 } \) moles.

It is defined as the force exerted by a gas on unit area of the wall
\(Pressure=\frac { Force }{ Area } \)
The SI unit of pressure is the Pascal (Pa), named after the French Mathematician and Physicist Blaise Pascal, and
1 Pa = 1 N m^-2
1 N = 1 Kg m s^-2

(i) Isotherm:
The pressure-volume curve at constant temperature are known as isotherm.
(ii) Isobar:
The volume - temperature curve at constant pressure are known as isobar.
(iii) Isochore:
The pressure-temperature curve at constant volume are known as isochore.

(i) The lowest hypothetical or imaginary temperature at which gases are supposed to occupy zero volume is called absolute zero.
(ii) Temperature below -273.15°C (absolute zero) is not possible, because it corresponds to negative volume, which is meaningless.

According to Avogadro's hypothesis: V \(\alpha\) n
\(\therefore \frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}=\text { constant }\)
V₁ & n₂ are the volume and number of moles of a gas and V₂ & n₂ are a different set of values of volume and number of moles of the same gas at same temperature and pressure.

Given data V₁ = 275 ml n₁ = 0.120 moles
V₂ = ?
\({ n }_{ 1 }=\frac { mass }{ molecular\ mass } =\frac { 1 }{ 44 } \)
Assuming pressure and temperature are constant According to Avogadro's hypothesis,
n₂ = 0.227 moles
\(\frac { { V }_{ 1 } }{ { n }_{ 1 } } =\frac { { V }_{ 2 } }{ { n }_{ 2 } } \)
\({ V }_{ 2 }=\frac { { V }_{ 1 }{ n }_{ 2 } }{ { n }_{ 1 } } \)
\({ V }_{ 2 }=\frac { 275\times 0.0227 }{ 0.120 } \)
V₂ = 52 moles
The volume of the balloon after dry ice has vaporized is V₁ + V₂ = 275 + 52 = 327 ml.