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Answer 1 · 2017-03-29T19:07:02

How about this?

Here's how to derive the law from Boyle's Law and Charles' Law.

Consider an ideal gas at conditions $p_1, V_1, T_1$ .

Now, keep $T$ constant and vary $p$ and $V$ to bring the gas to a second state $p_2 ,V ,T_1$ .

According to Boyle's Law:

(1) $p_1V_1 = p_2V$

Now, keep $p$ constant and vary $V$ and $T$ to bring the gas to a third state $p_1, V_2, T_2$ .

According to Charles Law,

(2) $V/T_1 = V_2/T_2$

From (1),

(3) $V = (p_1V_1)/p_2$

From (2)

(4) $V = (V_2T_1)/T_2$

Equating the right hand sides of (3) and (4), we get

$(p_1V_1)/p_2 = (V_2T_1)/T_2$

or

$(p_1V_1)/T_1 = (p_2V_2)/T_2 = k^'$ (a constant)

In general, we can write this as

$(pV)/T = k'$ or $p = (k^'/V)T$

Now, if we hold the volume $V$ constant, and let $k^'/V = k$ , we get

$p = kT$ ,

which is Gay-Lussac's Law.