91影视

Boyle鈥檚 law:According to Boyle鈥檚 law, 鈥渢he volume of the gas changes according to its pressure at constant temperature鈥�. It means that, at constant temperature, the volume of the gas is inversely proportional to its pressure.

$$\begin{gathered} V伪\frac{1}{P} \\ PV=cons\tan t(T,nfixed) \end{gathered}$$

Where, V = volume, T = temperature, P = pressure, n = number of moles

Charles鈥檚 Law: Accordingto Avogadro鈥檚 law, 鈥渁t constant temperature and pressure, the number of moles of gas is directly proportional to the volume鈥�.

$$\begin{gathered} V伪n \\ \frac{V}{n}=cons\tan t(P,Tfixed) \end{gathered}$$

Combining both laws,

According to Boyle鈥檚 law,

$\begin{array}{rcl}PV& =& cons\tan t(T,nfixed)\\ V& =& \frac{cons\tan t}{P}\end{array}$

Put above value in the Avogadro鈥檚 law,

$$\begin{gathered} \frac{V}{n}=cons\tan t(Avogadro\text{'}slaw) \\ \frac{{\displaystyle \frac{cons\tan t}{P}}}{n}=cons\tan t鈬�\frac{P}{n}=cons\tan t鈬�P伪n \end{gathered}$$

Thus, at constant temperature and volume, the pressure of the gas is directly proportional to the number of moles of the gas.