Problem 11
The gas inside a balloon will always have a pressure nearly equal to atmospheric pressure, since that is the pressure applied to the outside of the balloon. You fill a balloon with helium (a nearly ideal gas) to a volume of 0.600 L at 19.0\(^\circ\)C. What is the volume of the balloon if you cool it to the boiling point of liquid nitrogen (77.3 K)?
Problem 12
An ideal gas has a density of 1.33 \(\times\) 10\({^-}{^6}\) g/cm\(^3\) at 1.00 \(\times\) 10\({^-}{^3}\) atm and 20.0\(^\circ\)C. Identify the gas.
Problem 13
If a certain amount of ideal gas occupies a volume \(V\) at STP on earth, what would be its volume (in terms of \(V\)) on Venus, where the temperature is 1003\(^\circ\)C and the pressure is 92 atm?
Problem 14
A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.0\(^\circ\)C, and the temperature at the surface is 23.0\(^\circ\)C. (a) What is the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom? (b) Would it be safe for the diver to hold his breath while ascending from the bottom of the lake to the surface? Why or why not?
Problem 15
A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at 23.0\(^\circ\)C, to what temperature can the gas be warmed before the tank ruptures? Ignore the thermal expansion of the tank. (b) Based on your answer to part (a), is it reasonable to ignore the thermal expansion of the tank? Explain.
Problem 16
Three moles of an ideal gas are in a rigid cubical box with sides of length 0.300 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0\(^\circ\)C? (b) What is the force when the temperature of the gas is increased to 100.0\(^\circ\)C?
Problem 20
At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5\(^\circ\)C and the air density is 0.364 kg/m\(^3\). What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example 18.4 in Section 18.1 doesn't apply.)
Problem 21
How many moles are in a 1.00-kg bottle of water? How many molecules? The molar mass of water is 18.0 g/mol.
Problem 23
Modern vacuum pumps make it easy to attain pressures of the order of 10\({^-}{^1}{^3}\) atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00\(\times\) 10\({^-}{^1}{^4}\) atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm\(^3\)? (b) How many molecules would be present at the same temperature but at 1.00 atm instead?
Problem 27
(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m \(\times\) 12.00 m \(\times\) 4.00 m if the air is treated as an ideal gas at 1.00 atm? (b) What is the speed of a 2000-kg automobile if its kinetic energy equals the translational kinetic energy calculated in part (a)?
