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Chapter 16. Temperature and Expansion

16-1. Body temperature is normal at 98.60F. What is the corresponding temperature on the Celsius scale?
[pic]; tC = 370C

16-2. The boiling point of sulfur is 444.50C. What is the corresponding temperature on the Fahrenheit scale?
[pic]; tF = 8320F

16-3. A steel rail cools from 70 to 300C in 1 h. What is the change of temperature inFahrenheit degrees for the same time period?
Δt = 700C – 300C = 40 C0; [pic]; Δt = 72 F0

*16-4. At what temperature will the Celsius and Fahrenheit scales have the same numerical reading?
[pic]; x = -400C or –400F

16-5. A piece of charcoal initially at 1800F experiences a decrease in temperature of 120 F0. Express this change of temperature in Celsius degrees. What is thefinal temperature on the Celsius scale?
Δt = 120 F0; [pic]; Δt = 66.7 C0
The final temperature is 1800F – 120 F0 = 600F which must be converted to 0C:
[pic]; tC = 15.6 0C
16-6. Acetone boils at 56.50C and liquid nitrogen boils at -1960C. Express these specific temperatures on the Kelvin scale. What is the difference in these temperatures on the Celsius scale?
Acetone: T = tC+ 2730m = 56.50 + 2730; T = 329.5 K
Nitrogen: T = tC + 2730m = -1960 + 2730; T = 77.0 K
Δt = 56.50C – (-1960C) = 252.5 C0; Δt = 252.5 C0
Note: The difference in kelvins is the same as in Celsius degrees.

16-7. The boiling point of oxygen is –297.350F. Express this temperature in kelvins and in degrees Celsius.
[pic] tC = -1830C
T = tC + 2730 = -1830C + 2730; T =90.0 K

16-8. If oxygen cools from 1200 to 700F, what is the change of temperature in kelvins?
Δt = 1200F – 700F = 50 F0;
[pic]; 1 K = 1 C0; Δt = 27.8 K

16-9. A wall of firebrick has an inside temperature of 3130F and an outside temperature of 730F. Express the difference of temperature in kelvins.
Δt = 3130F – 730F = 240 F0;
[pic]; 1 K = 1 C0; Δt = 133 K
16-10. Gold meltsat 1336K. What is the corresponding temperature in degrees Celsius and in degrees Fahrenheit.
tC = 1336 K – 2730 = 10630C; tC = 10600C
[pic]; tF = 19500F

16-11. A sample of gas cools from –120 to -1800C. Express the change of
temperature in kelvins and in Fahrenheit degrees. [ Since 1 K = 1 C0, the change in kelvins is the same as in C0.]
Δt = -1800C – (-1200C) = -60 C0 ;ΔT = -60 K
[pic]; Δt = -108 F0

Temperature and Expansion
16-12. A slab of concrete is 20 m long. What will be the increase in length if the temperature changes from 120C to 300C. Assume that α = 9 x 10-6/C0.
[pic]; ΔL = 3.24 mm

16-13. A piece of copper tubing is 6 m long at 200C. How much will it increase in length when heated to 800C?
[pic]; ΔL = 6.12 mm

16-14. Asilver bar is 1 ft long at 700F. How much will it increase in length when it is placed into boiling water (2120F)?
[pic]; ΔL = 0.00156 ft
ΔL = 0.00156 ft(1 in./12 ft); ΔL = 0.0187 in.
16-15. The diameter of a hole in a steel plate 9 cm when the temperature is 200C. What will be the diameter of the hole at 2000C?
[pic]; ΔL = 0.0194 cm
L = L0 + ΔL = 9.00 cm + 0.0194 cm; L =9.02 cm

*16-16. A brass rod is 2.00 m long at 150C. To what temperature must the rod be heated so that its new length is 2.01 m? [ ΔL = 2.01 m – 2.00 m = 0.01 m ]
[pic]
t = to + Δt = 150C + 278 C0; t = 2930C

16-17. A square copper plate 4 cm on a side at 200C is heated to 1200C. What is the increase in the area of the copper plate? [ ( = 2α = 2(1.7 x 10-5/C0) = 3.4 x 10-5/C0]
ΔA = (AoΔt = (3.4 x 10-5/C0)(4 cm)2(1200C – 200C);
ΔA = 0.0544 cm2.

*16-18. A circular hole in a steel plate has a diameter of 20.0 cm at 270C. To what temperature must the plate be heated in order that the area of the hole be 314 cm2?
[pic] at 270C
The change in area must be 314 cm2 – 314.16 cm2: ΔA = - 0.16 cm
[pic]
Thus, the final temperature is 270C – 21.20C: t =...