Tippens Cap 16

Chapter 16. Temperature and Expansion

16-1. Body temperature is normal at 98.60F. What is the corresponding temperature on the Celsius scale?

; tC = 370C

16-2. The boiling point of sulfur is 444.50C. What is the corresponding temperature on the Fahrenheit scale?

; tF = 8320F

16-3. A steel rail cools from 70 to 300C in 1 h. What is the change of temperature in Fahrenheit degrees for the same time period?

t = 700C – 300C = 40 C0; t = 72 F0

*16-4. At what temperature will the Celsius and Fahrenheit scales have the same numerical reading?

; 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 the final temperature on the Celsius scale?

t = 120 F0; ; t = 66.7 C0

The final temperature is 1800F – 120 F0 = 600F which must be converted to 0C:

; 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

t = 56.50C – (-1960C) = 252.5 C0; t = 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.

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?

t = 1200F – 700F = 50 F0;

; 1 K = 1 C0; t = 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.

t = 3130F – 730F = 240 F0;

; 1 K = 1 C0; t = 133 K

16-10. Gold melts at 1336K. What is the corresponding temperature in degrees Celsius and in degrees Fahrenheit.

tC = 1336 K – 2730 = 10630C; t¬C = 10600C

; 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.]

t = -1800C – (-1200C) = -60 C0 ; T = -60 K

t = -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  = 9 x 10-6/C0.

; L = 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?

; L = 6.12 mm

16-14. A silver bar is 1 ft long at 700F. How much will it increase in length when it is placed into boiling water (2120F)?

; L = 0.00156 ft

L = 0.00156 ft(1 in./12 ft); L = 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?

; L = 0.0194 cm

L = L0 + L = 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? [ L = 2.01 m – 2.00 m = 0.01 m ]

t = to + t = 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? [  = 2 = 2(1.7 x 10-5/C0) = 3.4 x 10-5/C0 ]

A = Aot = (3.4 x 10-5/C0)(4 cm)2(1200C – 200C);

A = 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?

at 270C

The change in area must be 314 cm2 – 314.16 cm2: A = - 0.16 cm

Thus, the final temperature is 270C – 21.20C: t = 5.880C

16-19. What is the increase in volume of 16.0 liters of ethyl alcohol when the temperature is increased by 30 C0?

V = Vot = (11 x 10-4/C0)(16 L)(500C – 200C); V = 0.528 L

16-20. A Pyrex beaker has an inside volume of 600 mL at 200C. At what temperature will the inside volume be 603 mL? [ V = 603 mL – 300 mL = 3 mL ]

t = 200 C + 5560C; t = 5760C

16-21. If 200 cm3 of benzene exactly fills an aluminum cup at 400C, and the system cools to 180C, how much benzene (at 180C) can be added to the cup without overflowing?

t = (18 – 40) = -22 C0

V = (12.4 x 10-4 /C0)(200 cm3)(-22 C0) – 3(2.4 x 10-5/C0)(200 cm3)(-22 C)

V = -5.456 cm3 + 0.3168 cm3 = -5.14 cm3; VB = 5.14 cm3

16-22. A Pyrex glass beaker is filled to the top with 200 cm3 of mercury at 200C. How much mercury will overflow if the temperature of the system is increased to 680C?

Vo = 200 cm3; m = 1.8 x 10-4/C0; p = 0.3 x 10-5/C0

t = 680C – 200C = 48 C0;

V = (1.8 x 10-4 /C0)(200 cm3)(48 C0) – 3(0.3 x 10-5/C0)(200 cm3)(48 C0)

V = 1.728 cm3 – 0.0864 cm3 = 5.14 cm3; VB = 1.64 cm3

Challenge Problems

*16-23. The diameter of the hole in a copper plate at 200C is 3.00 mm. To what temperature must the copper be cooled if its diameter is to be 2.99 mm. [L = (2.99 – 3.00) = -0.01 mm ]

t = to + t = 200C - 196 C0; t = -1760C

16-24. A rectangular sheet of aluminum measures 6 by 9 cm at 280C. What is its area at 00C?

Ao = (6 cm)(9 cm) = 54 cm2; t = 00 – 280C = -280C ;  = 2

A = Aot = 2(2.4 x 10-5/C0)(54 cm2)(-28 C0) = -0.0726 cm2

A = 54 cm2 – 0.0726 cm2;

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