Explanation:
Direct Relationship - a mathematical relationship between two physical variables that depend upon one another such that when one variable increases the related variable also increases.
Example - For an enclosed gas it is observed that an increase in temperature (T) also results in an increase in pressure (P). Such is represented as P ∝ T which reads pressure (P) is directly related (or, proportional) to temperature (T). This does not mean that the variables temperature and pressure are equal, only that when one increases or decreases the other variable also increases or decreases proportionally.
Problems in Gas Laws relating pressure and temperature is typically referred to as The Gay-Lussac Law. Empirically it is represented by T₁/P₁ = T₂/P₂. Assume problem is given an enclosed gas at 25⁰C(= 298K*) and 750mm pressure. What is the pressure (P₂) if the temperature is increased to 35⁰C(= 308K)? and to 45⁰C(= 318K)?
*(Note: Problems in the empirical gas laws need to be worked in degrees Kelvin.)
T₁ = 25⁰C = 298K; P₁ = 750mm
T₂ = 35⁰C = 308K; P₂ = ?
T₃ = 45⁰C = 318K; P₃ = ?
T₁/P₁ = T₂/P₂ => P₂ = T₂·P₁/T₁ = 308K x 750mm / 298K = 775.17mm Pressure.
For P₃ calculation, one can work from either T₁,P₁ data or T₂,P₂ data.
This calculation chooses T₁,P₁ data.
T₁/P₁ = T₃/P₃ => P₃ = T₃·P₁/T₁ = 318K x 750mm / 298K = 800.34mm Pressure.
You apply T₂/P₂ = T₃/P₃ and you will find the same results for pressure.
Note that increasing temperature results in increasing pressure. This is 'direct relationship' analysis.
Dependent Variable & Independent Variable - The 'Dependent Variable' in a mathematical relationship 'Depends' upon an 'Independent Variable' which is chosen by the observer in order to determine the Dependent Variable. In the above problem, P is the dependent variable and T is the independent variable or, the variable the observer chooses to apply to the problem. Increases in Temperature (T) are chosen by observer to determine the Pressure (P). Increasing temperature (independent variable) results in increasing pressure (dependent variable).
Inverse Relationship - a mathematical relationship between two physical variables that depend upon one another such that when one variable increases the related variable decreases.
Example: A gas confined in a cylinder with a movable piston starting at Volume-1 (V₁) and at Pressure-1 (P₁) is changed to Volume-2 (V₂) will show a pressure value opposite to the direction of change (increased or decreased) to that of the volume change.
Problems in Gas Laws relating pressure and volume are typically referred to as Boyles Law problems. Empirically it is represented by V₁·P₁ = V₂·P₂. Assume problem is given an enclosed gas at 255ml and 750mm pressure. What is the pressure (P₂) if the volume is increased to 425ml? (Similar to pulling the plunger out of a syringe to increase volume.)
V₁ = 255ml; P₁ = 750mm
V₂ = 425ml; P₂ = ?
Using the Boyles Law relationship P₁V₁ = P₂V₂ => P₂ = P₁V₁ /V₂
P₂ = (750mm)(255ml)/(425ml) = 450mm
Note P₂ has a decreased pressure value which is opposite in direction to the change in the independent variable, volume-2 (V₂). That is, an increase in volume (V) resulted in a decrease in pressure (P).
Cyclic Change - Change that is repetitive or repeats within a noted (given) time interval. Weather change is cyclic in that fall => winter => spring => summer => fall => winter => etc.
Dynamic Equilibrium - In order to understand 'Dynamic Equilibrium' one must also define 'Static Equilibrium'. Static Equilibrium is when an object is not moving such as a marble sitting undisturbed on a level surface. All forces up, down, left & right are all equal. Dynamic Equilibrium is when an object is in motion at a constant speed on a level surface. All forces are also balanced forward, reverse, up & down. The term Dynamic Equilibrium is also applied to chemical reactions which means the rate of production of product is equal to the rate of production of reactant. This is typically represented by the equation Reactants ⇄ Products. the double arrow indicates a steady state condition of dynamic equilibrium.
