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## The Gas Equation

The three gas laws give the following equations:

pV = constant (when T is kept constant)
 V = constant (when p is kept constant) T
 p = constant (when V is kept constant) T

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