For a thermodynamics experiment I had to determine the ratio of the volumes of two tanks. The process used was isothermal. I pressurized up one tank and slowly opened the valve between the two tanks and let the pressure equalize. This experiment worked fine.
I was able to derive the necessary equation using the ideal gas law and considering the initial and final states of the two tanks:
$\frac{V_1}{V_2} = \frac{P_2}{P_1}$
Now I'm trying to do the same thing using an isobaric process. Pressurize the tanks up by the same amount and open the valve between them. But I can't seem to derive Charles' Law from the ideal gas equation. This is what I have so far:
Initial state of the two tanks: $PV_1 = M_1RT,\;PV_2 = M_2RT$
Final state of the two tanks: $PV_1 = M_3RT_1,\;PV_2 = M_4RT_2$
I can get to: $\frac{V_1}{V_2} = \frac{m_1}{m_2}$ or $\frac{V_1}{V_2} = \frac{m_3T_1}{m_4T_2}$
I'm aiming for:
$\frac{V_1}{V_2} = \frac{T_1}{T_2}$
Where am I going wrong?