Thermodynamics - Change in volume

[janiexo]

The next few questions refer to the Golden Great Bridge, built on planet Tehar in a galaxy far, far away. The bridge-building technology on Tehar is not very well developed: The bridge is just a long slab of pure gold with the opposite ends resting on the shores of the river.

In the spring, when the air temperature is 100 degrees Celsius, the length of the bridge is 160.0 klops (the klop is the unit of length on Tehar). Answer the questions below knowing that the value of alpha for gold is 1.4*10^-5.

Temperature in Winter: -150 degrees celcius
Temperature in Summer: 700 degrees celcius

By what percentage does the volume of the bridge increase between the winter and the summer?

I don't really know how to go about doing this question because it doesn't give the initial volume of the bridge. I tried to write 2 equations, one for the change in volume between winter and spring and another for the change in volume between spring and summer. I then canceled out the volume in spring in both equations and rearranged the combined equation to get volume in summer/volume in winter and got an answer of 1.04 which i * by 100 to get 104%, which was wrong. What is the proper way I'm meant to approach this question because that is the only way I can see to do it.

 

[nomorevishnu]

hi janiexo

the question is wrong i guess...because u have mentioned that bridge is just a long slab...so here there is no usa of talking abt its volume change throughout the year...the variation in length maybe a useful matter to discuss here...i think so...

 

[janiexo]

hi janiexo

the question is wrong i guess...because u have mentioned that bridge is just a long slab...so here there is no usa of talking abt its volume change throughout the year...the variation in length maybe a useful matter to discuss here...i think so...

The two questions before it were related to length:
*By what amount (deltaL) does the length of the bridge decrease during the Teharian winter when the temperature hovers around -150 degrees celcius
* By what amount does the length of the bridge increase during the Teharian summer when the temperature hovers around 700 degrees celcius?

I got them without too much problem, but the volume question is another matter :(

 

[Doc Al]

You can find by what percentage the length changes, without knowing the length using $L = L_0 (1 + \alpha \Delta T)$.

Do the same thing for the volume (which is $L^3$), realizing that since $\alpha$ is small you can ignore terms with higher powers of $\alpha$.

 

[janiexo]

I must not have understood because I got the same answer of 104%... or should it be 4% maybe? It says to "Express your answer as a percentage. Use three significant figures."

 

[Doc Al]

104 versus 4 = big difference! The percentage increase in volume is only about 4 percent, not 104!

Kind of strange to calculate the percentage change to 3 sig figs, when alpha is only given to 2 sig figs.

 

[janiexo]

Haha yep it was around 4%... I can't believe I did all of the hard work and didn't even know whether it should be 104% or 4%. Thanks for your help :)