Thermodynamics and Formula

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9. A concrete highway is built of slabs 14 m long (20Cº).  How wide should the expansion cracks be (at 20Cº) between the slabs to prevent buckling if the temperature range is -30Cº to +50Cº? I know I use the formula:

L  = LoT
L  = ? (Change in length of the slabs. We are solving for this.)     =  12e-6 (Coefficient of expansion. I looked it up on page 388.) Lo   =  14 m  (Initial length of slabs.)
T  =  30 Cº (50Cº - 20Cº)  (Change in temperaure.  You only care about the hottest number since you are dealing with expansion.) I then had the formula:
L = e14 m  30Cº
L = .00504 m
L = .50 cm
The space between the slabs must be the same as the expansion of the the slabs.  Therefore .50 cm is the correct answer. 17. A quartz sphere is 14.5 cm in diameter.  What will its change in volume if it is heated from 30Cº to 200Cº?  I had the formula:

V = VoT
V = ? (Volumetric change in the sphere.  We are solving for this.)      =  1e -6 (Cº)-1 (Coefficient of volumetric expansion.  It is on page 388 listed as .) Vo   =  (4/3) * (.145 m/2)3 (Initial volume.  You must take the diameter and divide by to to get the radius.  Then you must stick it in the formula for volume of a sphere: (4/3)r3 Vo   =  .001569 m3

T  =  170Cº (Change in temperature.  200Cº -  30Cº.) I then had the formula:
V = 1e-6*.001569m3*170Cº
V = 2.7 e-7 m3 *1e6 (Conversion from m3 to cm3.)
V = .27 cm3
The answer is therefore .27 cm3.

19. If the fluid is contained in a long, narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion  is approximately equal to the coefficient of volume expansion  (in the IB packet.)?  Since it can only expand in one direction, is is really linear expansion, not volumetric expansion. Therefore the two coefficients would be the same.

23. A 23.4 kg solid aluminum wheel of radius 0.52 m is rotating about its axel in frictionless bearings with an angular velocity 32.8...
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