Thermodynamics and Formula
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 = LoT
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 = e14 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 = VoT
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
I know I use the formula:
L = LoT
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 = e14 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 = VoT
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