please Explain the graphical representation of Boyle's law.
Boyle’s law states that the pressure exerted by a fixed amount of gas is inversely proportional to the volume occupied by the gas at constant temperature in a closed system.
Mathematically, this is represented as V = k (1)
This is an equation for a straight line, y =mx + c
Where m=slope of the line
c= intercept of the straight line
For Boyle’s Law equation,
y = V
x = 1/P
m=slope of the line
c=0
Graph 1 on the left is V vs 1/P
Equation 1 can be written as P = k 1/V
Graph is a straight line shown as graph 1 (right).
When P increases, V decreases and vice versa. This means that P and V are inversely related.
Therefore, P vs 1/V and V vs 1/P are direct relationships and thus increase in one will increase the other as well.
A straight line depicts linear or direct relationship.
The second type of graph is P vs V or V vs P
As there is an inverse relationship between pressure and volume, this graph is a hyperbola and is shown as number 2 on the figure.
The third type of plot is PV vs P and PV vs V
As, PV = constant k, the graph is a straight line parallel to x-axis (graph 3 in the figure)
Mathematically, this is represented as V = k (1)
This is an equation for a straight line, y =mx + c
Where m=slope of the line
c= intercept of the straight line
For Boyle’s Law equation,
y = V
x = 1/P
m=slope of the line
c=0
Graph 1 on the left is V vs 1/P
Equation 1 can be written as P = k 1/V
Graph is a straight line shown as graph 1 (right).
When P increases, V decreases and vice versa. This means that P and V are inversely related.
Therefore, P vs 1/V and V vs 1/P are direct relationships and thus increase in one will increase the other as well.
A straight line depicts linear or direct relationship.
The second type of graph is P vs V or V vs P
As there is an inverse relationship between pressure and volume, this graph is a hyperbola and is shown as number 2 on the figure.
The third type of plot is PV vs P and PV vs V
As, PV = constant k, the graph is a straight line parallel to x-axis (graph 3 in the figure)