# What equation encompasses Boyle's law and the relationship between pressure and temperature when the volume is constant?

May 4, 2014

Boyle's Law is a relationship between pressure and volume.

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

In this relationship, pressure and volume have an inverse relationship when temperature is held constant. If there is a decrease in the volume there is less space for molecules to move and therefore they collide more often, increasing the pressure. If there is an increase in the volume the molecules have more space to move, collisions happen less often and the pressure is decreased.

vV ^P ^V vP the relationship is inverse.

The relationship between pressure and temperature is the Gay-Lussac Law, in which Pressure and Temperature have a direct relationship as determined by the equation

$\frac{P}{T} = \frac{P}{T}$

Pressure and temperature will both increase or decrease simultaneously as long as the volume is held constant.

Therefore if temperature were to double the pressure would likewise double. Increased temperature would increase the energy of the molecules and the number of collisions would therefor increase causing an increase in temperature.

Take a sample of gas at STP 1 atm and 273 K and double the temperature.

$\frac{1 a t m}{273 K} = \frac{P}{546 K}$

$\frac{546 a t m K}{273 K} = P$

P = 2 atm

Doubling the temperature, likewise doubled the pressure.