Nice, that makes perfect sense. Thank you so much. Any idea on the other shapes question? Or is it just true that regardless of the shape, it's always approximately true that \DeltaV = 3\alphaVO\DeltaT, as long as the equation for linear expansion holds equally in every dimension.
Okay. I'm glad that I know it's an approximation. It bothers me, because my textbook (Y&F University Physics) didn't mention that detail WHATSOEVER, and in fact their proof is just plain incorrect; they made an illegal substitution that results in the coefficients being exact multiples.
Anyway...
Well, then how come in this proof it works out EXACTLY?
V = L3
dV/dL = 3L2
dL = \alphaLodT
dL/dT = \alphaLo
dV/dT = (dV/dL)(dL/dT) = 3L2 * \alphaLo = 3\alphaVo. Now just turn dV/dT into \DeltaV/\DeltaT (since dV/dT is constant, you can do that), and you have EXACTLY the equation.
It should...
Hi Physicsforums,
I was trying to derive the formula that the coefficient for volume expansion, β, is 3 times the coefficient for length expansion, \alpha.
As a reminder, the formulas are:
\DeltaL = \alphaLo\DeltaT
and \DeltaV = \betaVo\DeltaT
where, supposedly, \beta = 3\alpha...
Drakkith,
I'm currently an undergrad physics major. I'm aware that schooling in physics will help - I think that's a given. But if that were all it took, there would be many more successful theoretical physicists.
How to make a discovery in Physics/How to get in the "Physics Mindset"
Dear physicsforums,
Recently I've decided to take physics much more seriously, and - although this may sound lame - want to make a major discovery in physics. Ultimately, that's my goal. Don't tell me whether it's...