Copper Pipe Expansion: 2.5m Length Rise to 86.5°C

[tag16]

Homework Statement

A 2.5 m length of copper pipe extends directly from a hot-water heater in a basement to a faucet on the first floor of a house. If the faucet isn't fixed in place, how much will it rise when the pipe is heated from 20.0°C to 86.5°C. The coefficient of linear expansion for copper is 16 multiplied by10-6 K-1. Ignore any increase in the size of the faucet itself or of the water heater.

Homework Equations

D = deltaL = Lo*alpha*deltaT

The Attempt at a Solution

Used above equation to get 2.6mm but apparently that is wrong

 

[mgb_phys]

Do a rough estimate first before you hit the calculator,
Expansion of copper is roughly 20um/m per degree and you are heating it roughly 50 deg so about 1000um/m and you have 2.5m length so roughly 2.5mm is roughly correct.

Now that you know you are in the right range, just check how many decimal places they want the answer to - especially on those stupid web based answer things, so try 2.62mm
ps since you have 2sig figures in the data then 2sig fig in the answer is correct - whatever the teacher says!

 

[jmb]

Plugging the numbers in: the answer is 2.66 mm, so even if giving the answer to only 2 s.f. "2.6" would still be wrong! But what I really wanted to say...

ps since you have 2sig figures in the data then 2sig fig in the answer is correct - whatever the teacher says!

Actually significant figures are an extremely poor way to ensure your answer is accurate 'enough'. Students should never be encouraged to use them! For an explanation of why see e.g. the relevant sections of
http://www.av8n.com/physics/uncertainty.htm"
or any other good text on errors.

In this case in fact we aren't even explicitly told that 2.5 m is accurate to 2 s.f., it could be exact, or accurate to 5 decimal places for all we know! While the temperature is given to at least 3 s.f.

That said I agree that if I were marking this particular problem, I would take an answer of 2.7 as accurate enough (though I would prefer 2.66, it's always better to give a little more accuracy to be on the safe side).

Sorry to restart this thread so late, but I feel strongly that people should be dissuaded from ever using "significant figures" based arguments!