Page 246 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 19] EXPANSION OF SOLIDS, LIQUIDS, AND GASES 231

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3
19.10. At constant temperature the absolute pressure on 10 ft of air is increased from 20 to 80 lb/in. . The volume of the
air is now
(a) 2.5ft 3 (c) 40 ft 3
(b) 5 ft 3 (d) 80 ft 3

19.11. A sample of oxygen whose volume at 0 C and 200 kPa of pressure is 4.00 L is compressed to 1.00 L and its
◦
temperature is raised to 273 C. The pressure of the gas is now
◦
(a) 100 kPa (c) 800 kPa
(b) 400 kPa (d) 1600 kPa

Supplementary Problems

19.1. A steel bridge is 500 m long at 0 C. By how much does it expand when the temperature becomes 35 C? The
◦
◦
−5 ◦
coefficient of linear expansion of steel is 1.2 × 10 / C.
19.2. A brass rod 4 ft long expands by 1 in. when heated from 70 to 200 F. Find the coefficient of linear expansion of
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16
brass.
19.3. How much mercury (b = 1.8 × 10 / C) overflows when a glass vessel (b = 2 × 10 / C) filled to the brim with
−5 ◦
−4 ◦
3
◦
50 cm of mercury at 15 C is heated to 75 C?
◦
3
◦
19.4. The density of mercury is 830 lb/ft at 70 F. Find its density at 0 F. The coefficient of volume expansion of mercury
◦
−4 ◦
is 1.0 × 10 / F.
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19.5. A load of 2000 kg is placed on a vertical steel beam 5 m high whose cross-sectional area is 30 cm . The temperature
is 20 C. (a) By how much is the beam compressed? (b) At what temperature will the beam return to its original
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11
4
2
2
−5 ◦
height? For steel, Y = 2 × 10 Pa and a = 1.2 × 10 / F; 1m = 10 cm .
10
−5 ◦
19.6. Aluminum has a coefficient of linear expansion of 2.4 × 10 / C and a Young’s modulus of 7 × 10 Pa. For steel
−5 ◦
the respective values are 1.2 × 10 / C and 20 × 10 10 Pa. If identical bars of the two metals undergo the same
temperature change, which bar has the greater force associated with its change in length?
19.7. A compressor pumps 50 L of air at a pressure of 1 bar into an 8-L tank. What is the absolute pressure of the air in
the tank?
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19.8. How much air at a pressure of 1 bar can be stored in a 2-m tank which can safely withstand a pressure of 5 bar?
19.9. What is the Celsius equivalent of 500 K?
19.10. What is the Kelvin equivalent of 500 C?
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19.11. What is the Fahrenheit equivalent of 500 R?
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19.12. What is the Rankine equivalent of 500 F?
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2
19.13. A tire contains 1 ft of air at a gauge pressure of 28 lb/in. . How much additional air at atmospheric pressure must
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be pumped into the tire to raise the pressure to 36 lb/in. at the same temperature?
19.14. A tire contains air at a gauge pressure of 2 bar at 15 C. If the tire’s volume does not change, what will the gauge
◦
pressure be when its temperature is 38 C?
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