Boyles Law This is one question that has three parts. Please Help. A.) Given tha

Question

Boyles Law

This is one question that has three parts. Please Help.

A.) Given that two variables Z and Q are inversely related, write a simple mathematical equation that shows Z and Q on opposite sides of the equal sign with Z as the dependent variable (the one plotted on the vertical axis). Include a “constant” (a proportionality constant) as needed in your equation.

B.) Rewrite the mathematical equation so that Z and Q appear on the same side of the equation. Again, include a “constant” as needed.

C.) Of the two equations above, choose the one that resembles the general equation for a straight line (y = mx +b; y is the dependent variable and b may be zero). Assume that Z is measured in units of zips and Q in quips. Accurately sketch a plot in which the slope is equal to “2” (units omitted); assume the vertical intercept is at the origin.

Explanation / Answer

A) Z and Q are inversely related, i.e., Z 1/Q; the equality is given by

Z = K/Q …..(1)

where K is the proportionality constant.

Note that Z is here denoted as a dependent variable whose value depends on the value of Q.

B) Multiply both sides of expression (1) above by Q to obtain

Z*Q = K …..(2)

Here, both the variables appear on the same side of the equation.

C) Equation (1) above is linear, i.e, the equation is of the form y = mx + b where y = Z, x = 1/Q , m = K and b = 0.

Now, we have to plot a graph between Z and Q such that K = 2. We shall put values of Q and obtain values of Z using equation (1) above. Let us prepare a table with a few data points.

Q (quips)

1/Q (quips-1)

K

Z = K*1/Q (zips)

1

1

2

2

2

0.5

2

1

3

0.33

2

0.66

5

0.20

2

0.40

10

0.10

2

0.20

20

0.05

2

0.10

50

0.02

2

0.04

Now plot the graph.

Q (quips)

1/Q (quips-1)

K

Z = K*1/Q (zips)

1

1

2

2

2

0.5

2

1

3

0.33

2

0.66

5

0.20

2

0.40

10

0.10

2

0.20

20

0.05

2

0.10

50

0.02

2

0.04

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