19.1. a Constant-Volume Gas Thermometer Is Calibrated in Dry Ice (That Is, Carbon Dioxide

6E/S&J

19.1. A constant-volume gas thermometer is calibrated in dry ice (that is, carbon dioxide in the solid state, which has a temperature of –80.0°C) and in boiling ethyl alcohol (78.0°C). The two pressures are 0.900 atm and 1.635 atm. (a) What Celsius value of absolute zero does the calibration yield? What is the pressure at (b) the freezing point of water and (c) the boiling point of water?

19.6. On a Strange temperature scale, the freezing point of water is –15.0°S and the boiling point is +60.0°S. Develop a linear conversion equation between this temperature scale and the Celsius scale.

19.18. At 20.0°C, an aluminum ring has an inner diameter of 5.0000 cm and a brass rod has a diameter of 5.0500 cm. (a) If only the ring is heated, what temperature must it reach so that it will just slip over the rod? (b) If both are heated together, what temperature must they both reach so that the ring just slips over the rod? Would this latter process work?

19.20. A concrete walk is poured on a day when the temperature is 20.0°C in such a way that the ends are unable to move. (a) What is the stress in the cement on a hot day of 50.0°C? (b) Does the concrete fracture? Take Young’s modulus for concrete to be 7.00 x 109 N/m2 and the tensile strength to be 2.00 x 109 N/m2.

19.23. A steel rod undergoes a stretching force of 500 N. Its cross-sectional area is 2.00 cm2. Find the change in temperature that would elongate the rod by the same amount as the 500-N force does. Tables 12.1 and 19.1 are available to you.

19.24. The Golden Gate Bridge in San Francisco has a main span of length 1.28 km – one of the longest in the world. Imagine that a taut steel wire with this length and a cross-sectional area of 4.00 x 10-6 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 35.0°C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10.0°C, what is the tension in the wire? Take Young's modulus for steel to be 20.0 x 1010 N/m2. (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 108 N/m2. At what temperature would this happen? (c) How would your answers to (a) and (b) change if the Golden Gate Bridge were twice as long?

19.33. The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be heated before the balloon will lift off? (Air density at 10.0°C us 1.25 kg/m3.)

19.38. At 25.0 m below the surface of the sea (r = 1,025 kg/m3), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 1.00 cm3. If the surface temperature of the sea is 20.0°C, what is the volume of the air bubble just before it breaks the surface?

19.39. The pressure gauge on a tank registers the gauge pressure, which is the difference between the interior and exterior pressures. When the tank is full of oxygen (O2), it contains 12.0 kg of the gas at a gauge pressure of 40.0 atm. Determine the mass of the oxygen that has been withdrawn from the tank when the pressure reading is 25.0 atm. Assume that the temperature of the tank remains constant.

19.55. The rectangular plate shown in Figure P19.55 has an area Ai equal to lw. If the temperature increases by DT, each dimension increases according to the equation DL = aLiDT, where a is the average coefficient of linear expansion. Show that the increase in area is DA = 2aAiDT, where a is the average coefficient of linear expansion. What approximation does this expression assume?

19.62. Two concrete spans of a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P19.61a). If a temperature increase of DT occurs, what is the height y to which the spans rise when they buckle (Fig. P19.61b)?

19.64. (a) Use the equation of state for an ideal gas and the definition of the coefficient of volume expansion, in the form

to show that the coefficient of volume expansion for an ideal gas at constant pressure is given by

where T is the absolute temperature. (b) What value does this expression predict for b at 0°C? Compare this result with the experimental values for helium and air in Table 19.1. Note that these are much larger than the coefficients of volume expansion for most liquids and solids.

20.6. The Nova laser at Lawrence Livermore National Laboratory in California is used in studies of initiating controlled nuclear fusion (Section 45.4). It can deliver a power of 1.60 x 1013 W over a time interval of 2.50 ns. Compare its energy output in one such time interval to the energy required to make a pot of tea by warming 0.800 kg of water from 20.0°C to 100°C.

20.7 A 1.50 kg iron horseshoe initially at 600oC is dropped into a bucket containing

20.0 kg of water at 25.0 oC. What is the final temperature? (Ignore the heat capacity of the container, and assume that a negligible amount of water boils away.)