course Phy122
Ch.13 (1-5,7-9)1. How many atoms are there in a 3.4g copper penny?
- 1u=1.6605x10^-27kg copper= 62.929601u
62.929601u(1.6605x10^-27kg) = 1.04494602x10^-25kg (one atom of copper)
3.4g = .0034kg
.0034kg / 1.04494602x10^-25kg = 3.3x10^22 atoms in the penny
2. How does the number of atoms in a 26.5g gold ring compare to the number in a silver ring of the same mass?
- Gold Silver
196.966552u 106.905093u
196.966552u (1.6605x10^-27kg) 106.905093u (1.6605x10^-27kg)
= 3.2706296x10^-25 = 1.77515907x10^-25
.0265kg / 3.2706296x10^-25kg -.0265kg / 1.77515907x10^-25kg
= 8.10x10^22 atoms = 1.49x10^23 atoms
3. a) Room temp is often taken to be 68ºF. What’s this on the Celsius scale? b) The temp. of the filament in a lightbulb is about 1800ºC. What is this on the Fahrenheit scale?
- a) C=5/9(F-32) = 5/9 (68-32) = 57.8 ºC
-b) F=9/5C+32 = 9/5 (1800)+32 = 3272ºF
4. Among the highest and lowest tems. Recorded are 136ºF in the Libyan desert and -129ºF in Antarctica. What are these temps on the Celsius scale?
-C= 5/9(F-32) = 5/9(136-32) = 57.8ºC
-5/9 (-129-32) = -89.4ºC
5. a) 15º below zero on the Celsius scale is what Fahrenheit temp? b) 15º below on the Fahrenheit scale is what Celsius temp?
-a) F=9/5 (-15+32)= 30.6ºF
0 C corresponds to 32 F; however according to the formula you used here you would get F = 9/5(0 + 32) = 57.6 (if my mental arithmetic is correct).
You shouldn't try to remember this by formulas--too easy to confuse. You need only know two things:
0 C = 32 F
A F degree is 5/9 as large as a C degree.
Everything else can be reasoned out without the use of formulas.
-b) C=5/9(-15-32)= -26.1ºC
7. A concrete highway is built of slabs 12m long (20ºC). How wide should the expansion cracks between the slabs be (at 20ºC) to prevent buckling if the range of temp. is -30ºC to 50ºC?
- L=(fish looking symbol)L0∆T 12x10^-6(ºC)^-1(12m)(50-20) = .00432m
Because in -30 it contracts and needs less space so the only number necessary to look at is 50ºC.
8. Super Invar, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion (.02x10^-6(ºC)^-1). A 2.0m long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temp. increases 5.0ºC? Compare to tabletops made of steel.
- .02x10^-6(ºC)^-1(2m)(5ºC) = 2x10^-6m
-steel tabletops= 12x10^-6(ºC)^-1(2m)(5ºC) = 1.2x10^4 10^-4, not 10^4; just a typo but it makes a big difference
9. The Eiffel Tower is built of wrought iron approximately 300m tall. Estimate how much its height changes between July (avg. temp. of 25ºC) and January (avg. temp. of 2ºC). Ignore the angles of the iron beams, and treat the tower as a vertical beam.
-12x10^-6(ºC)^-1(300m)(25-2) = .0828m
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Good work. See my notes and let me know if you have questions.