Conceptual Questions:
1. Consider the ideal gas equation of state in the form P=NkT/V. Based on the
idea that a box containing gas is full of little particles moving about at random,
explain why the pressure should be proportional to each of these factors:
N, the number of particles in the box (and not their masses),
T, the temperature of the gas, and
1/V, the inverse volume of the box.
2. Which best describes the relationship between two systems in thermal equilibrium?
a. No net energy is exchanged.
b. The volumes are equal.
c. The masses are equal.
d. They have zero velocity.
3. The absolute (Kelvin) temperature of an ideal gas is directly proportional to which of the following properties of the molecules of that gas?
a. The average speed.
b. The average momentum.
c. The average mass.
d. The average kinetic energy.
4. Heat flow occurs between two bodies in thermal contact when they differ in what property?
a. mass
b. specific heat
c. density
d. temperature
Numerical Problems: answers link to a help page.
1. An ideal gas is confined to a container with adjustable volume. The number of moles and temperature are held constant. By what factor will the pressure change if the volume triples?
2. A two liter container holds half a mole of an ideal gas at a pressure of 12.5 atmospheres. What is the gas temperature? (R = 0.0821 liter*ATM/mole*K)
3. Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the molecular mass of nitrogen is 28, how many grams of nitrogen are present?
4. How many atoms are present in a sample of pure iron with a mass of 300 grams? The atomic mass of iron = 56 and NA = 6.02 x1023.
5. What is the root mean square velocity of chlorine gas molecules at a temperature of 320 K? R = 8.31 J/mole*K, NA = 6. 02 x1023, and the molecular mass of Cl2 molecules = 71.
6. Two moles of an ideal gas at 3 ATM and 10 øC are heated up to 150 øC. If the volume is held constant during this heating, what is the final pressure?
7. A pressure of 10-7 mm of Hg is achieved in a vacuum system. How many gas molecules are present per liter volume if the temperature is 293 K? 760 mm of Hg = 1 ATM, R = 0.081 liter*ATM/mole*K and NA = 6.02 x1023.
8. Normal body temperature for humans is 37 øC. What is this temperature in Kelvins?
9. How many moles of air must escape from a 10 m x 8 m x 5 m room when the temperature is raised from 0 øC to 20 øC at 1 ATM? Assume the pressure remains unchanged while the room is heated. No, this situation is not the same as rats leaving a sinking ship!
10. The mass of a hot air balloon and its cargo (not including the air inside) is 201 kg. The air outside is at a temperature of 10 øC and a pressure of 1 ATM = 105 N/m2. The volume of the balloon is a constant 400 m3. To what temperature must the air in the balloon be heated before the balloon will lift off? Air density at 10 øC is 1.25 kg/m3.
11. A spherical air bubble originating from a scuba diver at a depth of 18.0 m has a diameter of 1.0 cm. What will the bubble's diameter be when it reaches the surface? Assume constant temperature. Conceptual: will the temperature remain constant?