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physics
thermodynamics

Questions and Answers of Thermodynamics

Make the same assumptions as in Example 18.4 (Section 18.1). How does the percentage decrease in air pressure in going from sea level to an altitude of 100 m compare to that when going from sea level
With the assumptions of Example 18.4 (Section 18.1), how does the density of air at sea level compare to the density at an altitude of 100 m above sea level?
With the assumption that the air temperature is a uniform 0.0°C (as in Example 18.4), what is the density of the air at an altitude of 1.00 kin as a percentage of the density at the surface?
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/m3. What is the pressure of the atmosphere at that
A large organic molecule has a mass of 1.41 X 10-21 kg. What is the molar mass of this compound?
Suppose you inherit 3.00 mol of gold from your uncle (an eccentric chemist) at a time when this metal is selling for $14.75 per gram. Consult the periodic table in Appendix D and Table 14.1. (a) To
Modern vacuum pumps make it easy to attain pressures of the order of 10-13 atm in the laboratory. (a) At a pressure of 9.00 X 10-14 atm and an ordinary temperature of 300.0 K, how many molecules are
The Lagoon Nebula (Fig. 18.28) is a cloud of hydrogen gas located 3900 light-years from the earth. The cloud is about 45 light years in diameter and glows because of its high temperature of 7500 K.
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 6 X 109 people)?
How many moles are in a l.00-kg bottle of water? How many molecules? The molar mass of water is 18.0 g/mol.
How Close Together Are Gas Molecules? Consider an ideal gas at 27°C and 1.00 aim pressures. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly
Consider 5.00 mol of liquid water. (a) What volume is occupied by this amount of water? The molar mass of water is 18.0 g/mol(b) Imagine the molecules to be, on average, uniformly spaced, with each
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 and; (b) The root-mean-square speeds. (Hint: The
Gaseous Diffusion of Uranium (a) A process called gaseous diffusion is often used to separate isotopes of uranium that is, atoms of the elements that have different masses, such as 235U and 238U. The
The ideas of average and root-mean-square value can be applied to any distribution. A class of 150 students had the following scores on a 100-point quiz:(a) Find the average score for the class.(b)
We have two equal-size boxes, A and B. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box A is at a temperature of 50°C while the
The conditions of standard temperature and pressure (STP) are a temperature of 0.00°C and a pressure of 1.00 atm. (a) How many liters does 1.00 mol of any ideal gas occupy at STP? (b) For a
(a)A deuteron, 2/1H1 is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. What
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
(a) Oxygen (02) has a molar mass of 32.0 g/mol what is the average translational kinetic energy of an oxygen molecule at a temperature of 300 K? (b) What is the average value of the square of its
Calculate the mean free path of air molecules at a pressure of 3.50 X 10-13 atm and a temperature of 300 K. (This pressure is readily attainable in the laboratory; see Exercise 18.24.) As in Example
At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 20.0oC? (Hint: The periodic table in Appendix D shows the molar
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
(a) How much heat does it take to increase the temperature of 2.50 mol of a diatomic ideal gas by 30.0 K near room temperature if the gas is held at constant volume? (b) What is the answer to the
Perfectly rigid containers each hold n moles of ideal gas, one being hydrogen (H2) and other being neon (Ne). If it takes 100 j of heat to increase the temperature of the hydrogen by 2.50°C, by how
(a) Compute the specific heat capacity at constant volume of nitrogen (N2) gas, and compare with the specific heat capacity of liquid water. The molar mass of N2 is 28.0 g/mol (b) You warm 1.00 kg of
(a) Calculate the specific heat capacity at constant volume of water vapor, assuming the nonlinear triatomic molecule has three translational and three rotational degrees of freedom and that
(a) Use Eq. IS.2S to calculate the heat capacity at constant volume of aluminum in units of J /kg • K. Consult the periodic table in Appendix D. (b) Compare the answer in part (a) with the value
For a gas of nitrogen molecules (N2), what must the temperature be if 94.7% of all the molecules have speeds less than (a) 1500 m/s; (b) 1000 m/s; (c) 500 m/s? Use Table 18.2. The molar mass of N2
Derive Eq. (18.33) from Eq. (18.32).
Prove that f (v) as given by Eq. (18.33) is maximum for є = kT. Use this result to obtain Eq. (18.34).
For diatomic carbon dioxide gas ( CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (a) The most probable speed Ump; (b) The average speed Uav (c) The root-mean-square speed Urms.
Puffy cumulus clouds, which are made of water droplets, occur at lower altitudes in the atmosphere. Wispy cirrus clouds, which are made office crystals, occur only at higher altitudes. Find the
Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure P1 must be applied to the solid if a melting phase transition is to be observed? Describe the
A physicist places a piece of ice at 0.00oC and a beaker of water at 0.00oC inside a glass box and closes the lid of the box. All the air is then removed from the box. If the ice, water, and beaker
The atmosphere of the planet Mars is 95.3% carbon dioxide (CO2) and about 0.03% water vapor. The atmospheric pressure is only about 600 Pa, and the surface temperature varies from – 30oC to -100oC.
(a) Use Eq. (18.1) to estimate the change in the volume of a solid steel sphere of volume 11 L when the temperature and pressure increase from 21oC and 1.013 X l05 Pa to 42oC and 2.10 X 107 Pa.
A cylinder 1.00 m tall with inside diameter 0.120 m is used to hold propane gas (molar mass 44.1 g/mol) for use in a barbecue. It is initially filled with gas until the gauge pressure is 1.30 X 106
During a test dive in 1939, prior to being accepted by the U.S. Navy, the submarine Squalus sank at a point where the depth of water was 73.0 m. The temperature at the surface was27.0oC, and at the
Atmosphere of Titan. Titan, the largest satellite of Saturn, has a thick nitrogen atmosphere. At its surface, the pressure is 1.5 Earth-atmospheres and the temperature is 94 K. (a) What is the
Pressure on Venus. At the surface of Venus the average temperature is a balmy 460oC due to the greenhouse effect (global warming!), the pressure is 92 Earth-atmospheres, and the acceleration due to
An automobile tire has a volume of 0.0150 m3 on a cold day when the temperature of the air in the tire is 5.0oC and atmospheric pressure is 1.02 aims. Under these conditions the gauge pressure is
A flask with a volume of 1.50 L, provided with a stopcock, contains ethane gas (C2H6) at 300 K and atmospheric pressure (1.013 X l05 Pa). The molar mass of ethane is 30.1 g/mol. The system is warmed
A balloon whose volume is 750 m3 is to be filled with hydrogen at atmospheric pressure (1.01 X l05 Pa). (a) If the hydrogen is stored in cylinders with volumes of 1.90 m3 at a gauge pressure of 1.20
A vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 1.00 atm at 20.0oC. The round part of the tank has a radius of 10.0 cm, and the gas is supporting a piston that can
A large tank of water has a hose connected to it, as shown in Fig. 18.29. The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the
A person at rest inhales 0.50 L of air with each breath at a pressure of 1.00 atm and a temperature of 20.0°C. The inhaled air is 21.0% oxygen. (a) How many oxygen molecules does this person inhale
How Many Atoms Are Yon? Estimate the number of atoms in the body of a 50-kg physics student. Note that the human body is mostly water, which has molar mass 18.0 g/mol, and that each water molecule
The size of an oxygen molecule is about 2.0 X 10-10 m. Make a rough estimate of the pressure at which the finite volume of the molecules should cause noticeable deviations from ideal-gas behavior at
You have two identical containers, one containing gas A and the other gas B. The masses of these molecules arc m A = 3.34 X 10-27 kg and m B = 5.34 X 10-26 kg.Both gases arc under the same pressure
Insect Collisions. A cubical cage 1.25 m on each side contains 2500 angry bees, each flying randomly at 1.10 m/s. We can model these insects as spheres 1.50 cm in diameter. On the average, (a) How
Successive Approximations and the van der Waals Equation. In the ideal-gas equation, the number of moles per volume n/V is simply equal to p/RT. In the van der Waals equation, solving for n/V in
Gas on Europe. A canister of 1.20 mol of nitrogen gas (28.0 g/mol) at 25.0°C is left on Jupiter's satellite after completion of a future space mission. Europe has no appreciable atmosphere, and the
You blow up a spherical balloon to a diameter of 50.0 cm until the absolute pressure inside is 1.25 atm and the temperature is 22.0°C. Assume that all the gas in ~ is of molar mass 28.0 g/mol (a)
(a) Compute the increase in gravitational potential energy for a nitrogen molecule (molar mass 28.0 g/mol) for an increase in elevation of 400 m near the earth's surface. (b) At what temperature is
The Lennard-Jones Potential A commonly used potential energy function for the interaction of two molecules (see Fig. 18.8) is the Lennard-Jones 6-12 potentialWhere, is the distance between the
(a) What is the total random translational kinetic energy of 5.00 L of hydrogen gas (molar mass 2.016 g/mol) with pressure 1.01 X 105 Pa and temperature 300 K? (Hint: Use the procedure of Problem
(a) Urms for nitrogen molecules and (b) The rms value of Ux at this temperature. The molar mass of nitrogen (N2) is 28.0 g/mol
Hydrogen on the Sun The surface of the sun has a temperature of about 5800 K and consists largely of hydrogen atoms. (a) Find the rms speed of a hydrogen atom at this temperature. (The mass of a
(a) Show that a projectile with mass m can “escape” from the surface of a planet if it is launched vertically upward with a kinetic energy greater than mgRp, where g is the acceleration due to
Planetary Atmospheres (a) The temperature near the top of Jupiter's multicolored cloud layer is about 140 K. The temperature at the top of the earth's troposphere, at an altitude of about 20 km, is
(a) For what mass of molecule or particle is U = equal to 1.00 mm/s at 300 K? (b) If the particle is an ice crystal, how many molecules does it contain? The molar mass of water is 18.0 g/mol. (c)
In describing the heat capacities of solids in Section 18.4, we stated that the potential energy U = 1/2kx2 of a harmonic oscillator averaged over one period of the motion is equal to the kinetic
It is possible to make crystalline solids that are only one layer of atoms thick. Such “two-dimensional” crystals can be created by depositing atoms on a very flat surface. (a) If the atoms in
(a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300 K. (b) Calculate the moment of inertia of an oxygen molecule (O2) for rotation about either the
For each polyatomic gas in Table 18.1, compute the value of the molar heat capacity at constant volume, Cv, on the assumption that there is no vibrational energy. Compare with the measured values in
(a) Show that ∫∞0f (U) du = 1, where f (U) is the Maxwell-Boltzmann distribution of Eq. (18.32). (b) In terms of the physical definition of f (U), explain why the integral in part (a)
Calculate the integral in Eq. (18.31), ∫∞0 U2 f (U) du, and compare this result to (u2).v as given by Eq. (18.16). (Hint: You may use the tabulated integral
Calculate the integral in Eq. (18.30), ∫∞0 U f (U) du, and Compare this result to Uav as given by Eq. (18.35). (Hint: Make the change of variable v2 = x and use the tabulated integral
(a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval u to u + Δ u is Δ N = N f uu + Δuf(u) du. (b) If Δ u is small, then f (u)
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
The Dew Point The vapor pressure of water (see Problem 18.88) decreases as the temperature decreases. If the amount of water vapor in the air is kept constant as the air is cooled, a temperature is
Altitude at Which Clouds Form On a spring day in the Midwestern United States, the air temperature at the surface is 28.0°C. Puffy cumulus clouds form at an altitude where the air temperature equals
Dark Nebulae and the Interstellar Medium the dark area in Fig. 18.30 that appears devoid of stars is a dark nebula, a cold gas cloud in interstellar space that contains enough material to block out
Earth's Atmosphere In the troposphere, the part of the atmosphere that extends from earth's surface to an altitude of about 11 km, the temperature is not uniform but decreases with increasing
Van der Waals Equation and Critical Points (a) In p V- diagrams the slope ∂p/∂V along an isotherm is never positive. Explain why. (b) Regions where ∂p/∂V = 0 represent
In Example 18.7 (Section 18.3) we saw that Urms, > Vav. It is not difficult to show that this is always the case. (The only exception is when the particles have the same speed, in which case Urms =
Convert the following Celsius temperatures to Fahrenheit(a) -62.S0C, the lowest temperature ever recorded in North America (February 3, 1947, Snag, Yukon); (b) 56.7°C, the highest temperature ever
Find the Celsius temperatures corresponding to (a) A winter night in Seattle (41.0"F); (b) A hot summer day in Palm Springs (107.0°F); (c) A cold winter day in northern Manitoba (-18.0°F).
While vacationing in Italy, you see on local TV one summer morning that the temperature will rise from the current 18°C to a high of 39°C. What is the corresponding increase in the Fahrenheit
Two beakers of water, A and B, initially are at the same temperature. The temperature of the water in beaker A is increased 10 Fo, and the temperature of the water in beaker B is increased 10K.After
You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 10.0 K. What is its temperature change in? (a) Fo and (b) Co?
(a) On January 22, 1943, the temperature in Spearfish, South Dakota, rose from -4.0°F to 45.0°F in just 2 minutes. What was the temperature change in Celsius degrees? (b) The temperature in
(a) You feel sick and are told that you have a temperature of 40.2°C. What is your temperature in oF? Should you be concerned? (b) The morning weather report in Sydney gives a current temperature of
(a) Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other. (b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each
Convert the following record-setting temperatures to the Kelvin scale: (a) The lowest temperature recorded in the 48 contiguous states (-70.0°F at Rogers Pass, Montana, on January 20, 1954); (b)
Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) The midday temperature at the surface of the moon (400 K); (b) The temperature at the tops of the clouds in the
Liquid nitrogen is a relatively inexpensive material that is often used to perform entertaining low-temperature physics demonstrations. Nitrogen gas liquefies at a temperature of - 346°F. Convert
A 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
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?
Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0oR). However, the units of this scale are the same size as 1hose of the Fahrenheit
A Constant-Volume Gas Thermometer An experimenter using a gas thermometer found the pressure at the triple point of water (0.01°C) to be 4.80 X l04Pa and the pressure at the normal boiling point
The tallest building in the world, according to some architectural standards, is the Taipei l01 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the
The Humber Bridge in England has the world's longest single span.1410m.Calculate the change in length of the steel deck of the span when the temperature increases from-5.0oC to 18.oC.
Ensuring a Tight Fit. Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by “dry ice” (solid CO2) before being driven. If the diameter of a
A U.S. penny has a diameter of 1.9000 cm at 20.0°C. The coin is made of a metal alloy (mostly zinc) for which the coefficient of linear expansion is 26 X 10-5 K-1. What would its diameter be on a
A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of - 15°C. How much more interior space does the
A metal rod is 40.125 cm long at20.0°C and 40.148 cm long at 45.0°C. Calculate the average coefficient of linear expansion of the rod for this temperature range.
A copper cylinder is initially at 20.0oC. At what temperature will its volume be 0.150% larger than it is at 20.0oC?
The density of water is 999.73 kg/m3 at a temperature of 10°C and 958.38 kg/m3 at a temperature of 100°C. Calculate the average coefficient of volume expansion for water in that range of

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