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Thermal Expansion of Solids and Liquids

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  1. From base to torch, the Statue of Liberty is 46.1 m tall. How much taller is the monument on a 25 °C summer day than on a 2.2 °C winter day? (The Statue of Liberty is made of copper; its coefficient of thermal expansion is 16.7 × 10-6/°C.)
  2. A cat’s water dish is left outside overnight, where it fills to the brim with water during a thunderstorm. If the dish holds 227 mL of water, how many milliliters of water will overflow from the dish if the temperature rises by 10.3 °C during the day? (The volumetric coefficient of expansion for water varies greatly with temperature; consider it to be 210 × 10-6/°C at the temperatures that occur this day.)
  3. The manufacturing process for an automobile part involves drilling a hole 13.9 mm in diameter into a steel plate. By how many millimeters will the diameter of the hole grow when the engine is running, causing the part’s temperature to rise from 69 °F to 112 °F? (The coefficient of thermal expansion for steel is 12 × 10-6/°C.)
  4. Suppose that a bridge is built from pieces of concrete 4.46 m long. If the gaps between pieces are 5.18 mm on a fall day with temperature 15 °C, at what temperature would the pieces of concrete begin to touch one another? (Use a value of 9.5 × 10-6/°C for the coefficient of thermal expansion of concrete.)
  5. A traveler fills her gas tank with 13.72 gallons of gas in the heat of the day, when the temperature is 87.4 °F. How many gallons will be in her tank later that night, when the temperature has dropped to 68.1 °F? (Gasoline’s coefficient of volumetric expansion is 950 × 10-6/°C.)
  6. The coefficient of thermal expansion of wood varies greatly depending on the type of wood and direction of the grain. Suppose that a wooden meter stick shrinks by 0.14 mm when it is taken to a 11.5 °C location for an outdoor lab experiment. If the inside temperature was 21 °C, what is the meter stick’s coefficient of thermal expansion?

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