Boyle's Law - Experiment Question

[charlottexo]

Hey guys, I was just wondering if you could help me on this quick question I have.

Homework Statement

A student does an experiment to investigate Boyle's Law by adding masses onto the bottom of an upside down syringe and measuring the length of the gas column in the syringe. Force is calculated from the masses using an equation, and logF is plotted against logL on a graph.

The student suggests that using a longer but thinner syringe (with the same unloaded volume), would be an advantage experiment. Discuss whether you agree with this notion.

Homework Equations

F = (P0 x A) - Mg, where M is the added mass, A is the cross-sectional area of the syringe and P0 is atmospheric pressure.

The Attempt at a Solution

I definitely know that the longer/thinner syringe would give rise to greater values of L, and so the uncertainty in L will be reduced.

However, the uncertainty in A would increase, as the cross sectional area is smaller. This introduces more uncertainty in the force.

My query mainly is that, would it be an advantage overall? Given that L is measured using a standard metre rule, and A is given to us (measured using vernier callipers). Given also that A only needs to be measured once and L is measured multiple times, which presents more opportunity for uncertainty.

I would think that having a factor of higher uncertainty in A would be less of an issue, as the uncertainty is quite low to start with and so, the overall uncertainty in the experiment would be less with a longer/thinner syringe.

I definitely know like I said, that uncertainty in L is reduced so there is an advantage with those measurements. Can anyone perhaps help me expand on this though?

Thanks!

 

[rude man]

Using V = πD²L/4, compute dV/V in terms of dD/D and dL/L. This gives you the fractional error in V given fractional errors in L and D. Then use worst-case or root-mean-square assumption to make your decision.

Hint: think limiting case where D << L.

 

[charlottexo]

Thanks for the reply but er... that seems a bit beyond me I think. I'm doing UK A-level Physics so basically it's meant to be an easy common sense answer really, and it is worth 2 marks.

I think it just wants a general comment, and I'm pretty sure half of that comment is, reduced uncertainty in measurement of L.

I then need to make another point and say, overall it is an advantage/disadvantage to use a longer/thinner syringe.