# Formulas

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.

##
Contents:

## Boyle's Law:

Boyle's law is described by the two following formulas: PV = *k*, where
k is a constant; P_{1}V_{1} = P_{2}V_{2}.

The derivative of the first formula: P'V + PV' = 0

The derivative of the second formula: P_{1}'V_{1} + P_{1}V_{1}'
= P_{2}'V_{2} + P_{2}V_{2}'

With appropriate manipulation, one can arrive at a solution for a particular
variable.

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## Charles' Law:

Charles' Law is described by the following equations: V/T = *k *(Again,
k is constant) and V_{1}/T_{1} = V_{2}/T_{2}.

The derivative of the first is: (V'T - T'V) / T^{2} = 0

The derivative of the second is: (V_{1}'T_{1} - T_{1}'V_{1})
/ (T_{1})^{2 = }(V_{2}'T_{2} - T_{2}'V_{2})
/ (T_{2})^{2}

One quick note: If you examine the first listed derivative, you will notice a
variable will drop out (the T^{2}), and this introduces error into the
solutions.

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## Combined Gas Law:

The Combined Gas Law is described by the following equations: (PV) / T = k
and (P_{1}V_{1}) / T_{1} = (P_{2}V_{2})
/ T_{2}

The derivative of the first is: ((P'V + V'P)T - T'PV) / T^{2} = 0

The derivative of the second is: ((P_{1}'V_{1} + V_{1}'P_{1})T_{1}
- T_{1}'P_{1}V_{1}) / (T_{1})^{2} = ((P_{2}'V_{2}
+ V_{2}'P_{2})T_{2} - T_{2}'P_{2}V_{2})
/ (T_{2})^{2}

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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