Let's review how we would put together our three theories mathematically:
Step 1: We would write them one by one:
\(P = m_1 \times N\) (Eq. 1)
\(P = m_2 \times T\) (Eq. 2)
\(P = {m_3 \over V}\) (Eq. 3)
Step 2: We would combine the right side of the equations:
\(P = {{(m_1 \times N) \times (m_2 \times T) \times (m_3)} \over V}\) (Eq. 4)
Step 3: We would slightly modify the equation by moving \(V\) to the other side of the equation and we would also get rid of the parentheses:
\(P \times V = {m_1 \times m_2 \times m_3 \times N \times T }\) (Eq. 5)
Finally, we would combine all three coefficients \((m_1 \times m_2 \times m_3)\)as one coefficient, which we can simply call as \(m_g\) or the ideal gas coefficient:
\(P \times V = {m_g \times N \times T }\) (Eq. 6)
