HW#13a Note: numbers used in solution steps are different from your WebAssign values. Page 1 of 8

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1 Note: numbers used in solution steps are different from your WebAssign values. Page 1 of 8 Note: numbers used in solution steps are different from your WebAssign values. 1. Walker3 17.P.003. [565748] Show Details In the morning, when the temperature is 286 K, a bicyclist finds that the absolute pressure in his tires is 501 kpa. That afternoon he finds that the pressure in the tire has increased to 554 kpa. Ignoring expansion of the tires, find the afternoon temperature. 316K When total amount and volume is not changed, Pressure is proportional to Temperature. p/t=constant. 2. Walker3 17.P.008. [565980] Show Details A balloon contains 3.7 liters of nitrogen gas at a temperature of 87 K and a pressure of 101 kpa. If the temperature of the gas is allowed to increase to 24 C and the pressure remains constant, what volume will the gas occupy? 13L When total amount and pressure is not changed, Volume is proportional to Temperature. V/T=constant. 3. Walker3 16.P.007. [565730] Show Details The gas in a constant-volume gas thermometer has a pressure of 91.5 kpa at 101 C. (a) What is the pressure of the gas at 50.0 C? kpa (b) At what temperature does the gas have a pressure of 115 kpa? C

2 Note: numbers used in solution steps are different from your WebAssign values. Page 2 of 8 When total amount and volume is not changed, Pressure is proportional to Temperature. p/t=constant. p 1 /T 1 = p 2 /T 2, so also (p 1 - p 2 ) / (T 1 -T 2 ) = p 1 /T 1 = p 2 /T 2, this is the rate at which pressure increases as a function of temperature. 4. Walker3 16.P.011. [565718] Show Details When the bulb of a constant-volume gas thermometer is placed in a beaker of boiling water at 100 C, the pressure of the gas is 227 mmhg. When the bulb is moved to an ice-salt mixture the pressure of the gas drops to 162 mmhg. Assuming ideal behavior, as in the figure below, what is the Celsius temperature of the ice-salt mixture? C

3 Note: numbers used in solution steps are different from your WebAssign values. Page 3 of 8 5. Walker3 17.P.013. [565750] Show Details The air inside a hot air balloon has an average temperature of 77.2 C. The outside air has a temperature of 20.3 C. What is the ratio of the density of air in the balloon to the density of air in the surrounding atmosphere? inside / outside = Please notice that at balanced condition, pressure is equal inside and out of the hot air balloon. Otherwise, if pressure outside is higher, the balloon will shrink and air will keep flowing in through the opening forever. If pressure inside is higher, air will keep flowing out through the opening forever. As a result, at balanced situation, pressure in and out is the same. Initially some cold air was in the balloon; later that part of air is heated up. V increases as T increases. And the change of V leads to the change of density. Math again, how is density related to V for given amount of material? Remember density=mass/volume Especially if you know the volume ratio of V1/V2, how is the ratio of density1/density2? Remember that for same amount of air, the larger Volume, the lower the density.

4 Note: numbers used in solution steps are different from your WebAssign values. Page 4 of 8 6. Walker3 17.P.015. [565769] Show Details A cylindrical flask is fitted with an airtight piston that is free to slide up and down, as shown in the figure below. Contained within the flask is an ideal gas at a constant temperature of 313 K. Initially the pressure applied by the piston and the mass is 137 kpa, and the height of the piston above the base of the flask is 23.4 cm. When additional mass is added to the piston, the height of the piston decreases to 20.0 cm. Find the new pressure applied by the piston. 160kPa When total amount and Temperature is not changed, pv=constant. 7. Walker3 17.P.017. [566037] Show Details If the molecules in a tank of H 2 have the same rms speed as the molecules in a tank of Oxygen, select all of the following statements about which we may be certain. The pressures are the same. The H 2 is at the higher pressure. The oxygen is at the higher pressure. The temperatures are the same. The H 2 is at the higher temperature. The oxygen is at the higher temperature. Justify your answer. Key: The total internal energy due to thermal motion is 3/2 * NkT, for N particles. The average thermal motion energy for each gas molecule is ½ (mv 2 ) avg =3/2 kt, hence, we have expression (mv 2 ) avg = 3kT. If we know that the have same average rms speed, we know that the temperature (and internal energy) is proportional to the mass, and H 2 is less massive than carbon dioxide. Mass of per H 2 molecule is less than mass per carbon dioxide molecule.

5 Note: numbers used in solution steps are different from your WebAssign values. Page 5 of 8 8. Walker3 17.P.020. [565857] Show Details Three moles of oxygen gas (O 2 ) are placed in a portable container with a volume of m 3. The temperature of the gas is 295 C. (a) What is the pressure of the gas? Pa (b) What is the average kinetic energy of an oxygen molecule? J (c) Suppose the volume of the gas is doubled, while the temperature and number of moles are held constant. By what factor do your answers to parts (a) and (b) change? P new = P old 0.5 K new = K old 1 Explain. Key: Pressure is inversely proportional to volume, whereas the average kinetic energy per molecule depends only upon the temperature.

6 Note: numbers used in solution steps are different from your WebAssign values. Page 6 of 8 9. Walker3 17.P.026. [565647] Show Details A 350 ml spherical flask contains mol of an ideal gas at a temperature of 293 K. What is the average force exerted on the walls of the flask by a single molecule? 2.8e-19N Due to math abilities, it may be difficult for you to do all those algebra suggested above before plugging in numbers. As a result, I SUGGEST YOU TO solve this problem STEP BY STEP. 1, You can solve for pressure using pv=nrt. Plug in all numbers in SI unit and get pressure in unit Pa. 2, Once you solve for p you know that the total force on the inner wall of the sphere flask is F total = p*a. The total area of a sphere is A=4*pi*r 2, where r is the radius of the sphere. 3. You were not told the r, but you were told the total volume of the sphere. You should know from basic geometry that for spheres, V= (4/3)*pi*r 3. See step 3 above. Be careful when you solve the radius. If you use cm 3 as the volume unit, (milliliter, ml), you get the radius in the unit of cm, and you need to convert it to meter for calculating area, A. If you use m 3 as the volume unit, you get the radius in the unit of meter. Attention that 350ml =0.35 L= 0.35*10 3 m 3. In order to get force in the unit of Newton, you will need to use SI unit for volume, area, pressure, and length 4, Total force on the inner wall of the sphere flask is F total = p*a. All particles contribute to it. 5. You know the number of moles n, and you will need the Avogadro s number per mole N A =6.022*10 23 to calculate the total amount of molecules. N=n* N A 6, Once you have the total force, divided by the total number of molecules, you know the force per particle. Force per particle = F total /N To solve problems step by step helps you to clear your mind and help you to get partial credits.

7 Note: numbers used in solution steps are different from your WebAssign values. Page 7 of Walker3 17.P.053. [565908] Show Details The figure shows the temperature of kg of water as heat is added to the system. Suppose that such a sample of water starts at point A at time zero. Heat is added to this system at the rate of J/s. Calculate the time for the system to reach each of the following points. (a) B s (b) C s (c) D s (d) Describe the physical state of the system at time t = 63 s. ice ice and water water steam water and steam

8 Note: numbers used in solution steps are different from your WebAssign values. Page 8 of Walker3 18.CE.003. [612730] You plan to add a certain amount of heat to a gas in order to raise its temperature. If you add the heat at constant volume, is the increase in temperature greater than, less than, or the same as if you add the heat at constant pressure? greater than less than equal to Explain. Key: You get a greater increase in temperature when you add the heat at constant volume. At constant pressure, the gas expands and does work as the heat is added. Hence, only part of the heat goes into increasing the internal energy. When heat is added at constant volume no work is done. In this case, all the heat goes into increasing the internal energy, and hence the temperature. 12. Walker3 18.CQ.002. [613896] The temperature of a substance is held fixed. (a) Is it possible for heat to flow into this system? yes Key: Heat can flow into the system if at the same time the system expands, as in an isothermal expansion of a gas. Heat flows in is equal to the amount of work done by the system, so that internal Energy and Temperature don t change. (b) Is it possible for heat to flow out of this system? yes Key: Heat can flow out of the system if at the same time the system is compressed, as in an isothermal compression of a gas. Heat flows out is equal to the amount of work done to the system by the outside surroundings, so that internal Energy and Temperature don t change. 13. Walker3 18.CQ.003. [614133] A substance is thermally insulated, so that no heat can flow between it and its surroundings. (a) Is it possible for the temperature of this substance to increase? yes Key: Compress a gas in a thermally insulated cylinder. This will cause its temperature to rise. The system doesn t absorb or give off heat, but the surroundings do work to the system, to increase its inner energy, hence increase the Temperature. (b) Is it possible for the temperature of this substance to decrease? yes Key: If you expand a gas in a thermally insulated cylinder, its temperature will decrease. The system doesn t absorb or give off heat, but the system does work to the surroundings to reduce its inner energy, hence reduces the Temperature. It is opposite to question a. 14. Walker3 18.CQ.005. [613862] Show Details The temperature of a substance is increased. Is it safe to conclude that heat was added to the substance? no Key: One cannot conclude that heat was added to the system, because it is not known whether any work was done to the system by the surroundings. For example, if a gas in a thermally insulated cylinder is compressed, its temperature will rise with no heat transfer.