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Chapter 13 Solutions
College Physics
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- An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)arrow_forwardOne of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?arrow_forwardA company advertises that it delivers helium at a gauge pressure of 1.72107 Pa in a cylinder of volume 43.8 L. How many balloons can be inflated to a volume of 4.00 L with that amount of helium? Assume the pressure inside the balloons is 1.72105 Pa and the temperature in the cylinder and the balloons is 25.0 .arrow_forward
- For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?arrow_forwardAn aluminum rod 0.500 m in length and with a cross sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 3(H) K. (a) If one-halt of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool, (b) If the circular surface of the upper end of the rod is maintained at 300 K. what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 YV/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)arrow_forwardA certain ideal gas has a molar specific heat of Cv = 72R. A 2.00-mol sample of the gas always starts at pressure 1.00 105 Pa and temperature 300 K. For each of the following processes, determine (a) the final pressure, (b) the final volume, (c) the final temperature, (d) the change in internal energy of the gas, (e) the energy added to the gas by heat, and (f) the work done on the gas. (i) The gas is heated at constant pressure to 400 K. (ii) The gas is heated at constant volume to 400 K. (iii) The gas is compressed at constant temperature to 1.20 105 Pa. (iv) The gas is compressed adiabatically to 1.20 105 Pa.arrow_forward
- Why is the following situation impossible? An ideal gas undergoes a process with the following parameters: Q = 10.0 J, W = 12.0 J, and T = 2.00C.arrow_forwardThe measurement of the average coefficient of volume expansion for a liquid is complicated because the container also changes size with temperature. Figure P19.62 shows a simple means for measuring despite the expansion of the container. With this apparatus, one arm of a U-tube is maintained at 0C in a water-ice bath, and the other arm is maintained at a different temperature Tc in a constant-temperature bath. The connecting tube is horizontal. A difference in the length or diameter of the tube between the two arms of the U-tube has no effect on the pressure balance at the bottom of the tube because the pressure depends only on the depth of the liquid. Derive an expression for for the liquid in terms of h0, hi and Tc.arrow_forwardWhat is the internal energy of 6.00 mol of an ideal monatomic gas at 200 ?arrow_forward
- On a hot summer day, the density of air at atmospheric pressure at 35.0C is 1.1455 kg/m3. a. What is the number of moles contained in 1.00 m3 of an ideal gas at this temperature and pressure? b. Avogadros number of air molecules has a mass of 2.85 102 kg. What is the mass of 1.00 m3 of air? c. Does the value calculated in part (b) agree with the stated density of air at this temperature?arrow_forwardA high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.40 x 107 N/m² and a temperature of 16.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperatures (-78.5°C), to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? 9.42e6 N/m² (b) What is the final pressure if one-tenth of the gas escapes? 8.61e6 N/m² (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? 2.14 Review the values for initial and final pressure for this situation. Karrow_forwardA high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.60 107 N/m2 and a temperature of 12.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperatures (−78.5°C), to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? N/m2(b) What is the final pressure if one-tenth of the gas escapes? N/m2(c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)?arrow_forward
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