# Math Help - please! tricky logs (i think!) question.

1. ## please! tricky logs (i think!) question.

hiya

this is a really horrible q i'd dearly love some advice for.
Q: Gas expands in a space according to a law "P=CV^n"
P is pressure kNm^-2, V is volume m^3, C and n are constants.
an experiment produces these results
P: 100 | 200 | 300 | 400 | 500
V: 0.165 | 0.104 | 0.079 | 0.064 | 0.055
a) explain carefully how you would plot a graph to verify P and V follow a relationship according to the above law; what would be plotted on each axis?
b)supposing a straight line on the graph passes through the first and last data points, find the values of C and n in this example. there is no need to plot an accurate graph here.

thanks so so much!

2. Originally Posted by synnr
hiya

this is a really horrible q i'd dearly love some advice for.
Q: Gas expands in a space according to a law "P=CV^n"
P is pressure kNm^-2, V is volume m^3, C and n are constants.
an experiment produces these results
P: 100 | 200 | 300 | 400 | 500
V: 0.165 | 0.104 | 0.079 | 0.064 | 0.055
a) explain carefully how you would plot a graph to verify P and V follow a relationship according to the above law; what would be plotted on each axis?
plot the P on the y-axis and the V on the x-axis.

b)supposing a straight line on the graph passes through the first and last data points, find the values of C and n in this example. there is no need to plot an accurate graph here.
for the first point, you have P = 100, and V = 0.165, thus you have the relationship: $100 = C(0.165)^n$

for the last point, you have P = 500 and V = 0.055, thus you have the relationship: $500 = C(0.055)^n$

thus you need to solve the system:

$100 = C(0.165)^n$ .........................(1)
$500 = C(0.055)^n$ ..........................(2)

for $C$ and $n$

incidentally, this is probably how I'd deduce that the relationship works in part (1), solve for C and n between each pair of points, but that may be too tedious. you may be able to tell what, say n is by the shape of the graph. if it is like a parabola, you know n = 2, for example