This Topic Contains

The Gas Equation

The three gas laws give the following equations:

pV = constant (when T is kept constant)

Boyle’s Law

V	= constant (when p is kept constant)
T

Charles’ Law

p	= constant (when V is kept constant)
T

Pressure Law

These 3 equations are combined to give the ideal gas equation:

pV	= constant
T

Where,

p = the pressure of the gas
V = the volume the gas occupies
T = the gas temperature on the Kelvin scale

From this equation we know that if a fix mass of gas has starting values of p1, V1 and T1, and then some time later has value p2, V2 and T2, the equation can be written as:

p₁V₁	=	p₂V₂
T₁	=	T₂

Example:

Sabah pumps up her front bicycle tyre to 1.7 x 10⁵ Pa. The volume of air in the tyre at this pressure is 300 cm³. She takes her bike for a long ride during which the temperature of the air in the tyre increases from 20°C to 30°C. Calculate the new front tyre pressure assuming the tyre had no leaks and so the volume remained constant?

Solution:

p₁ = 1.7 x 10⁵ Pa
T₁ = 20°C = 20 + 273 = 293 K
V₁ = 300 cm³

p₂ = ?
T₂ = 30°C = 30 + 273 = 303 K
V₂ = 300 cm³

Using:

p₁V₁ = p₂V₂

T₁ T₂

Rearranging for P2

p₂ = p₁V₁T₂

V₂T₁

We know V1 = V2, therefore the equation can be simplified to:

p₂ = p₁T₂

T₁

p₂ = 1.7 x 10⁵ x 303

293

p₂ = 1.76 x 10⁵Pa