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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.