Question

Question #28264

Answer 1

How about this?

Explanation:

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.