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Review. This problem is a continuation of Problem 16.29 in Chapter 16. A hot-air balloon consists of an envelope of constant volume 400 m3. Not including the air inside, the balloon and cargo have mass 200 kg. The air outside and originally inside is a diatomic ideal gas at 10.0°C and 101 kPa, with density 1.25 kg/m3. A propane burner at the center of the spherical envelope injects energy into the air inside. The air inside stays at constant pressure. Hot air, at just the temperature required to make the balloon lift off, starts to fill the envelope at its closed top, rapidly enough so that negligible energy flows by heat to the cool air below it or out through the wall of the balloon. Air at 10°C leaves through an opening at the bottom of the envelope until the whole balloon is filled with hot air at uniform temperature. Then the burner is shut off and the balloon rises from the ground. (a) Evaluate the quantity of energy the burner must transfer to the air in the balloon. (b) The “heat value” of propane—the internal energy released by burning each kilogram—is 50.3 MJ/kg. What mass of propane must be burned?
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Principles of Physics: A Calculus-Based Text
- 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_forwardA 40.0-g projectile is launched by the expansion of hot gas in an arrangement shown in Figure P12.4a. The cross sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 52 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are P1 = 11 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.0 105 Pa and Vf = 8.0 cm3. Friction between the projectile and the launch tube is negligible, (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? (b) If instead the projectile is launched into air at a pressure of 1.0 105 Pa. what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down tile tube?arrow_forwardCylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forward
- A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68arrow_forwardReview. This problem is a continuation of Problem 39 in Chapter 19. A hot-air balloon consists of an envelope of constant volume 400 m3. Not including tire air inside, the balloon and cargo have mass 200 kg. The air outside and originally inside is a diatomic ideal gas at 10.0C and 101 kPa, with density 1.25 kg/m3. A propane burner at the center of the spherical envelope injects energy into the air inside. The air inside stays at constant pressure. Hot air, at just the temperature required to make the balloon lift off, starts to fill the envelope at its closed top, rapidly enough so that negligible energy flows by heat to the cool air below it or out through the wall of the balloon. Air at 10C leaves through an opening at the bottom of the envelope until the whole balloon is filled with hot air at uniform temperature. Then the burner is shut off and the balloon rises from the ground. (a) Evaluate the quantity of energy the burner must transfer to the air in the balloon. (b) The heat value of propanethe internal energy released by burning each kilogramis 50.3 MJ/kg. What mass of propane must be burned?arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P21.65). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state, (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally, (f) Find Q, W, and Eint for each of the processes, (g) For the whole cycle A B C A, find Q, W, and Eint.arrow_forward
- Under constant pressure, the temperature of 2.00 mol of an ideal monatomic gas is raised 15.0 K. What are (a) the work W done by the gas, (b) the energy transferred as heat Q, (c) the change Eint in the internal energy of the gas, and (d) the change K in the average kinetic energy per atom?arrow_forwardConsider neon, a noble gas whose molecules consist of single atoms of atomic mass 0.02 kg/mol. What is the average kinetic energy of a neon atom when the gas is at a temperature of 260 K? Avogadro’s number is 6.02 × 1023 mol−1 and Boltzmann’s constant is 1.38 × 10−23 J/K. Answer in units of J What is the root mean square speed of a neon atom under such conditions? Answer in units of m/s. The internal energy of a monoatomic ideal gas such as neon is simply the total kinetic energy of all its atoms. What is the internal energy of 4 liters of neon at a temperature of 260 K and pressure of 0.89 atm? Answer in units of J.arrow_forward2.00-mol of a monatomic ideal gas goes from State A to State D via the path A→B→C→D: State A PA=13.0atm, VA=13.00L State B PB=13.0atm, VB=6.00L State C PC=24.5atm, VC=6.00L State D PD=24.5atm, VD=21.50L Assume that the external pressure is constant during each step and equals the final pressure of the gas for that step. Calculate q for this process. Calculate w for this process .Calculate ΔE for this process Calculate ΔH for this process.arrow_forward
- Five moles of gas initially at a pressure of 2.00 atm and a volume of 0.300 L has internal energy equal to 91.0 J. In its final state, the gas is at a pressure of 1.50 atm and a volume of 0.800 L, and its internal energy equals 182 J. Three paths are plotted on a PV diagram, which has a horizontal axis labeled V (liters), and a vertical axis labeled P (atm). The green path starts at point I (0.300,2.00), extends vertically down to point A(0.300,1.50), then extends horizontally to point F (0.800,1.50). The blue path starts at point I (0.300,2.00), and extends down and to the right to end at point F (0.800,1.50). The orange path starts at point I (0.300,2.00), extends horizontally to the right to point B (0.800,2.00), then extends vertically down to end at point F (0.800,1.50). (a) For the paths IAF, IBF, and IF in the figure above, calculate the work done on the gas. WIAF = J WIBF = J WIF = J (b) For the paths IAF, IBF, and IF in the figure above, calculate the net energy…arrow_forwardA sealed cubical container 11.0 cm on a side contains a gas with five times Avogadro's number of neon atoms at a temperature of 25.0°C. (a) Find the internal energy (in J) of the gas. J (b) The total translational kinetic energy (in J) of the gas. J (c)Calculate the average kinetic energy (in J) per atom.J (d)Use P = 2 3 N V 1 2 mv2 to calculate the gas pressure (in Pa). (e)Calculate the gas pressure (in Pa) using the ideal gas law (PV = nRT). Paarrow_forward2.00-mol of a monatomic ideal gas goes from State A to State D via the path A→B→C→D: State A PA=10.5atm, VA=13.50L State B PB=10.5atm, VB=6.00L State C PC=20.5atm, VC=6.00L State D PD=20.5atm, VD=25.00L Assume that the external pressure is constant during each step and equals the final pressure of the gas for that step. A) Calculate q for this process B) Calculate w for this process C) Calculate ΔE for this process D) Calculate ΔH for this process Express answer in L atm units!arrow_forward
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