Thermodynamics HW-4(“Ideal Gases & Kinetic Theory”): due______

Read pp.362–372

Conceptual Questions

1.(a) Is the number of molecules in one mole of greater than, less than, or equal to the number of molecules in one mole of Explain. (b) Which of these has the greater mass? Explain.

2.Is the number of atoms in one mole of carbon greater than, less than, or the same as the number of atoms in one mole of oxygen gas (O2)? Explain.

3.If you put a helium-filled balloon in the refrigerator, will its volume increase, decrease, or stay the same? Explain.

4.Plastic bubble wrap is used as packing material. Is the bubble wrap more or less effective on a cold day than on a warm day? Explain.

5.Two containers hold ideal gases at the same temperature. Container B has twice the volume and half the number of molecules as container A. How does the pressure of container B compare with that of container A? Explain.

6.How is the air pressure in a tightly sealed house affected by operating the furnace? Explain.

7.At the beginning of a typical airline flight you are instructed about the proper use of oxygen masks that will fall from the ceiling if the cabin pressure suddenly drops. You are advised that the oxygen masks are working properly, even if the bags do not fully inflate. In fact, the bags expand to their fullest if cabin pressure is lost at high altitude, but expand only partially if the plane is at low altitude. Explain.

8.Is it possible to change both the pressure and the volume of an ideal gas without changing the average kinetic energy of its molecules? If your answer is no, explain why not. If your answer is yes, give a specific example.

9.The average speed of air molecules in your room is on the order of the speed of sound. What is their average velocity?

10.The air in your room is composed mostly of oxygen (O2) and nitrogen (N2) molecules. The oxygen molecules are more massive than the nitrogen molecules. How do their rms speeds compare?

11.Two adjacent rooms in a hotel are equal in size and connected by an open door. One of the rooms is warmer than the other. Which room contains more air? Explain.

12.As you go up in altitude, do you expect the ratio of oxygen to nitrogen in the atmosphere to increase, decrease, or stay the same? Explain.

13.If the translational speed of molecules in an ideal gas is doubled, by what factor does the Kelvin temperature change? Explain.

14.One of the highest airports in the world is located in La Paz, Bolivia. Pilots prefer to take off from this airport in the morning or the evening, when the air is quite cold. Explain.

15.Suppose the Celsius temperature of an ideal gas is doubled from 100 °C to 200 °C. Does the average kinetic energy of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2? Explain.

16.Suppose the absolute temperature of an ideal gas is doubled from 100 K to 200 K. Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2? Explain.

Problems

Ideal Gases

1.In the morning, when the temperature is 288 K, a bicyclist finds that the absolute pressure in his tires is 505 kPa. That afternoon he finds that the pressure in the tire has increased to 552 kPa. Ignoring expansion of the tires, find the afternoon temperature.

2.The Goodyear blimp Spirit of Akron is 62.6 m long and contains of helium. When the temperature of the helium is 285 K, its absolute pressure is 112 kPa. Find the mass of the helium in the blimp.

3.A typical region of interstellar space may contain atoms per cubic meter (primarily hydrogen) at a temperature of 100 K. What is the pressure of this gas?

4.A balloon is filled with helium at a pressure of The balloon is at a temperature of 18 °C and has a radius of 0.25 m. (a) How many helium atoms are contained in the balloon? (b) Suppose we double the number of helium atoms in the balloon, keeping the pressure and the temperature fixed. By what factor does the radius of the balloon increase? Explain.

5.A flask contains 0.460 g of a gas at a pressure of 153 kPa and a temperature of 322 K. What is the molar mass, M, of this gas?

6.A cylindrical flask is fitted with an airtight piston that is free to slide up and down, as shown in the figure below. A mass rests on top of the piston. 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 (and therefore the new pressure of the enclosed gas).

Kinetic Theory

7.At what temperature is the rms speed of equal to the rms speed that has at 303 K?

8.Suppose a planet has an atmosphere of pure ammonia at 0.0 °C. What is the rms speed of the ammonia molecules? (hint: look up the chemical formula of ammonia and the masses of its constituent atoms.)

9.The rms speed of is 1550 m/s at a given temperature. (a) Is the rms speed of at this temperature greater than, less than, or equal to 1550 m/s? Explain. (b) Find the rms speed of at this temperature.

10.What is the temperature of a gas of molecules whose rms speed is 339 m/s?

Answers

1. 315 K

2. 1.33 x 103 kg

3. 1.4 x 10-15 Pa

4. (a) 3.9 x 1024 atoms (b) increase factor = (r2 – r1)/r1 = 0.26 or 26%

5. 15.6 g/mol or .0156 kg/mol

6. 160. kPa

7. 19.1 K

8. vrms = 632 m/s

9. (a)The rms speed of is more than the rms speed of because…explain. (b) vrms = 2070 m/s

10. T = 203 K