Listed below are the formula's for the gas laws, and their derivatives.
For the sake of space conservation, I will not be using the dx notation, but
rather the f '(x) notation. Also, each function will not be solved for any
specific variable or rate.
Boyle's law is described by the two following formulas: PV = k, where
k is a constant; P1V1 = P2V2.
The derivative of the first formula: P'V + PV' = 0
The derivative of the second formula: P1'V1 + P1V1'
= P2'V2 + P2V2'
With appropriate manipulation, one can arrive at a solution for a particular
Charles' Law is described by the following equations: V/T = k (Again,
k is constant) and V1/T1 = V2/T2.
The derivative of the first is: (V'T - T'V) / T2 = 0
The derivative of the second is: (V1'T1 - T1'V1)
/ (T1)2 = (V2'T2 - T2'V2)
One quick note: If you examine the first listed derivative, you will notice a
variable will drop out (the T2), and this introduces error into the
Combined Gas Law:
The Combined Gas Law is described by the following equations: (PV) / T = k
and (P1V1) / T1 = (P2V2)
The derivative of the first is: ((P'V + V'P)T - T'PV) / T2 = 0
The derivative of the second is: ((P1'V1 + V1'P1)T1
- T1'P1V1) / (T1)2 = ((P2'V2
+ V2'P2)T2 - T2'P2V2)
Below are some general physics formulas as related to forces. Again, I
will not use the dx notation to save space.
Position, Velocity, Acceleration
Position in relation to time is defined: d(t) = vt
The first derivative of position is: v(t) =
Copyright 2001-2003, James P. Hansen