# The relationships between n , T , P , V for a gas?

The symbols :

T : temperature // V : volume // P : pressure // n : number of mole

what it is clearly known about the relationship between one another is :

P is inversely proportional to V ( from Boyle's law : PV=constant )

V is directly proportional to T ( from Charles's law : V/T=constant )

but the other ones I am not sure about them, So i might say :

P is inversely proportional to T

T is inversely proportional to n

p is directly proportional to n

What do you think?

All statements like "P is inversely proportional to V" should be qualified with "other variables being equal". With this qualification you can read off all the proportionalities from $pV=NRT$. Any two variables on the same side are inversely proportional; any two on opposite sides are directly proportional. So $p$ is directly proportional to $T$. Your other assertions are correct.
Just remember the general gas law $$\mathrm{PV=nRT}$$ or rearranging terms we see that $$\mathrm{\frac{[PV]}{[nT]}=R}$$ where R is a constant. Therefore, $$\mathrm{\frac{[P_1V_1]}{[n_1T_1]}=\frac{[P_2V_2]}{[n_2T_2]}}$$
this very general set of ratios relates all of the variables in state (1) to the same variables in state (2). If volume and number of moles don't change, then the equation reduces to $$\mathrm{\frac{[P_1]}{[T_1]}=\frac{[P_2]}{[T_2]}}$$ and so on and so forth. All of the proportionalities are clearly layed out in one general equation.