Question

PLEASE HELPP!!!!


Combine Boyle’s law, Charles’ law, and Gay-Lussac’s law to express a single proportional relationship between pressure (P), volume (V), and temperature (T).

Answer 1

Answer:

The combined law is:

          $\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

See the derivation below.

Explanation:

1. Boyle's law:

    $PV=constant\\\\P_1V_1=P_2V_2$

2. Charles' law:

        $\dfrac{V}{T}=constant\\\\\\\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$

3. Gay-Lussac’s law

      $\dfrac{P}{T}=constant\\\\\\\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}$

4. Summary:

•    PV = K

•    V/T = K'

•    P/T = K''

Mulitply PV by V/T and P/T

        $PV\times \dfrac{V}{T}\times \dfrac{P}{T}=K\times K'\times K''\\\\\\\dfrac{P^2V^2}{T^2}=constant\\\\\\\sqrt{\dfrac{P^2V^2}{T^2}}=\sqrt{constant}\\\\\\\dfrac{PV}{T}=constant$

Thus:

          $\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

Which is the combined law.