Ch 18: Thermal Properties of Matter
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Problem 17
The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?Problem 17
A constant-volume gas thermometer registers an absolute pressure corresponding to 325 mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?Problem 18
Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0°C, is warmed until both pressure and volume are doubled. (a) What is the final temperature?Problem 18
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m^3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m^3. If the temperature remains constant, what is the final value of the pressure?Problem 18
Planetary Atmospheres. (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere), and Saturn's moon Titan (where the pressure is 1.5 atm and the temperature is -178°C, with a N2 atmosphere).Problem 18
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°C and the pressure is 92 atm?Problem 18
At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5°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 18
How many moles are in a 1.00-kg bottle of water? How many molecules? The molar mass of water is 18.0 g/molProblem 18
A large organic molecule has a mass of 1.41 * 10^-21 kg. What is the molar mass of this compound?Problem 18
Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00 * 10^-14 atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm^3?Problem 18
Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (b) How many molecules would be present at the same temperature but at 1.00 atm instead?Problem 18
In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7 * 10^9 people)?Problem 18
How Close Together Are Gas Molecules? Consider an ideal gas at 27°C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?Problem 18
Meteorology. The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature, expressed as a percentage. The air is saturated when the humidity is 100%. (a) The vapor pressure of water at 20.0°C is 2.34 * 10^3 Pa. If the air temperature is 20.0°C and the relative humidity is 60%, what is the partial pressure of water vapor in the atmosphere (that is, the pressure due to water vapor alone)?Problem 18
How much heat does it take to increase the temperature of 1.80 mol of an ideal gas by 50.0 K near room temperature if the gas is held at constant volume and is (a) diatomic;Problem 18
How much heat does it take to increase the temperature of 1.80 mol of an ideal gas by 50.0 K near room temperature if the gas is held at constant volume and is (b) monatomic?Problem 18
(a) Compute the specific heat at constant volume of nitrogen (N2) gas, and compare it with the specific heat of liquid water. The molar mass of N2 is 28.0 g/mol.Problem 18
(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m * 12.00 m * 4.00 m if the air is treated as an ideal gas at 1.00 atm?Problem 18
A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (a) the average kinetic energies of the three types of atoms andProblem 18
Calculate the mean free path of air molecules at 3.50 * 10^-13 atm and 300 K. (This pressure is readily attainable in the laboratory; see Exercise 18.23.) As in Example 18.8, model the air molecules as spheres of radius 2.0 * 10^-10 m.Problem 18
A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)Problem 18
Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (a) the rms speeds of the CO2 molecules andProblem 18
Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (b) the density (in mol/m^3) of the atmosphere?Problem 18
Oxygen (O2) has a molar mass of 32.0 g>mol. What is (a) the average translational kinetic energy of an oxygen molecule at a temperature of 300 K;Problem 18
Oxygen (O2) has a molar mass of 32.0 g>mol. What is (d) the momentum of an oxygen molecule traveling at this speed?Problem 18
At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 20.0°C? (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element. The molar mass of H2 is twice the molar mass of hydrogen atoms, and similarly for N2.)Problem 18
Smoke particles in the air typically have masses of the order of 10-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the rootmean-square speed of Brownian motion for a particle with a mass of 3.00 * 10-16 kg in air at 300 K.Problem 18
For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (a) the most probable speed v_mp;Problem 18
For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (b) the average speed v_av;Problem 18
For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (c) the root-mean-square speed v_rms.
