The units for the coefficient of linear expansion a are

Solution 7CQ The atmospheric pressure for each point in the liquid is same. Only difference in pressure comes from the depth of a particular point in the liquid from the surface (since P = hdg, h is the depth here).

A concrete highway is built of slabs 12 m long \((20^\circ~\mathrm C)\). How wide should the expansion cracks between the slabs be (at \(20^\circ~\mathrm C\)) to prevent buckling if the range of temperature is \(-30^\circ~\mathrm C\) to \(+50^\circ~\mathrm C\)?

Problem8CQ The atmospheric pressure for each point in the liquid is same. Only difference in pressure comes from the depth of a particular point in the liquid from the surface (since P = hdg, h is the depth here).

Problem 8P Super Invar™, an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion (0.20 X 10-6/C°). A 1.8-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this alloy table expand along its length if the temperature increases 6.0 C°? Compare to tabletops made of steel.

Problem 21P (a) The tube of a mercury thermometer has an inside diameter of 0.140 mm. The bulb has a volume of 0.255 cm3. How far will the thread of mercury move when the temperature changes from 11.5°C to 33.0°C? Take into account expansion of the Pyrex glass. (b) Determine a formula for the change in length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

Problem 22P A 23.4-kg solid aluminum cylindrical wheel of radius 0.41 m is rotating about its axle on frictionless bearings with angular velocity ? = 32.8 rad/s. If its temperature is now raised from 20.0°C to 75.0°C, what is the fractional change in ??

(II) An aluminum bar has the desired length when at \(15^{\circ} \mathrm{C}\). How much stress is required to keep it at this length if the temperature increases to \(35^{\circ} \mathrm{C}\) ?

Problem 24P (a) A horizontal steel I-beam of cross-sectional area 0.041 m2 is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30°C, what stress is developed in the beam when the temperature drops to ?30°C? (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13 m2? Will it fracture?

(I) What are the following temperatures on the Kelvin scale: (a) \(86^{\circ} \mathrm{C}\), (b) \(78^{\circ} \mathrm{F}\), (c) \(-100^{\circ} \mathrm{C}\), (d) \(5500^{\circ} \mathrm{C}\), (e) \(-459^{\circ} \mathrm{F}\)?

Problem 27P Absolute zero is what temperature on the Fahrenheit scale?

(II) Typical temperatures in the interior of the Earth and Sun are about \(4000^{\circ} \mathrm{C}\) and \(15 \times 10^6{ }^{\circ} \mathrm{C}\), respectively. (a) What are these temperatures in kelvins? (b) What percent error is made in each case if a person forgets to change \({ }^{\circ} \mathrm{C}\) to \(\mathrm{K}\) ?

Problem 29P (I) If 3.50 m3 of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0°C. What is the volume?

(I) In an internal combustion engine, air at atmospheric pressure and a temperature of about \(20^{\circ} \mathrm{C}\) is compressed in the cylinder by a piston to \(\frac{1}{9}\) of its original volume (compression ratio =9.0 ). Estimate the temperature of the compressed air, assuming the pressure reaches \(40 \mathrm{~atm}\).

Problem 31P Calculate the density of oxygen at STP using the ideal gas law.

Problem 32P A storage tank contains 21.6 kg of nitrogen (N2) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of CO2 ?

Problem 34P If 18.75 mol of helium gas is at 10.0°C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions. (b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

Problem 35P What is the pressure inside a 35.0-L container holding 105.0 kg of argon gas at 385 K?

Problem 37P A hot-air balloon achieves its buoyant lift by heating the air inside the balloon, which makes it less dense than the air outside. Suppose the volume of a balloon is 1800 m3 and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0°C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.)

Problem 36P A tank contains 26.0 kg of O2 gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?

Problem 38P A tire is filled with air at 15°C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38°C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?

Problem 2Q Name several properties of materials that could be used to make a thermometer.

Problem 3Q Which is larger, 1 C° or 1 F°? Explain why.

Problem 4P Among the highest and lowest natural air temperatures claimed are 136°F in the Libyan desert and-129°F in Antarctica. What are these temperatures on the Celsius scale?

Problem 5P (a) 18° below zero on the Celsius scale is what Fahrenheit temperature? (b) 18° below zero on the Fahrenheit scale is what Celsius temperature?

A flat bimetallic strip consists of a strip of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Why?

Problem 7Q The units for the coefficient of linear expansion a are (Co)-1 and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure shows a diagram of a simple thermostat used to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

(I) The Eiffel Tower (Fig. 13-29) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of \(25^\circ{C}\)) and January (average temperature of \(2^\circ{C}\)). Ignore the angles of the iron beams and treat the tower as a vertical beam.

Problem 9Q Long steam pipes that are fixed at the ends often have a section in the shape of a U. Why?

Problem 12Q A glass container may break if one part of it is heated or cooled more rapidly than adjacent parts. Explain.

The principal virtue of Pyrex glass is that its coefficient of linear expansion is much smaller than that for ordinary glass (Table 13-1). Explain why this gives rise to the higher increased heat resistance of Pyrex.

Problem 14P It is observed that 55.50 mL of water at 20°C completely fills a container to the brim. When the container and the water are heated to 60°C, 0.35 g of water is lost, (a) What is the coefficient of volume expansion of the container? (b) What is the most likely material of the container? Density of water at 60°C is 0.98324 g/mL.

Problem 15Q Freezing a can of soda will cause its bottom and top to bulge so badly the can will not stand up. What has happened?

Problem 17Q Will the buoyant force on an aluminum sphere submerged in water increase, decrease, or remain the same, if the temperature is increased from 20°C to 40°C? Explain.

Is it possible to boil water at room temperature \((20^\circ {C}\)) without heating it? Explain.

Problem 26Q Explain why it is dangerous to open the radiator cap of an overheated automobile engine.

Why does exhaled air appear as a little white cloud in the winter (Fig. 13-28)?

Problem 41P Calculate the number of molecules/m3 in an ideal gas at STP.

(II) Estimate the number of (a) moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 Km.

Problem 47P Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000 K.

(I) A gas is at \(20^{\circ} \mathrm{C}\). To what temperature must it be raised to triple the rms speed of its molecules?

Problem 1P How many atoms are there in a 3.4-gram copper penny?

Problem 1Q Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the Periodic Table or Appendix B.

(I) How does the number of atoms in a 26.5-gram gold ring compare to the number in a silver ring of the same mass?

Problem 53P Show that the rms speed of molecules in a gas is given by i!mls = VJPjp. where P is the pressure in the gas and is the gas density.

(I) (a) “Room temperature” is often taken to be \(68^{\circ} \mathrm{F}\). What is this on the Celsius scale? (b) The temperature of the filament in a lightbulb is about \(1800^{\circ} \mathrm{C}\). What is this on the Fahrenheit scale?

Problem 4Q If system A is in thermal equilibrium with system B, but B is not in thermal equilibrium with system C, what can you say about the temperatures of A, B, and C?

Problem 60P Two isotopes of uranium, 235U and 238U (the superscripts refer to their atomic masses), can be separated by a gas diffusion process by combining them with fluorine to make the gaseous compound UF6. Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T. Use Appendix B for masses.

Problem 6P In an alcohol-in-glass thermometer, the alcohol column has length 11.82 cm at 0.0°C and length 22.85 cm at 100.0°C. What is the temperature if the column has length (a) 16.70 cm, and (b) 20.50 cm?

(I) (a) At atmospheric pressure, in what phases can \(\mathrm{CO}_{2}\) exist? (b) For what range of pressures and temperatures can \(\mathrm{CO}_{2}\) be a liquid? Refer to Fig. 13-21. Equation Transcription: Text Transcription: C0_2 C0_2

In the relation \(\Delta L=\alpha L_0 \ \Delta T\), should \(L_0\) be the initial length, the final length, or does it matter? Explain.

(I) Water is in which phase when the pressure is 0.01 atm and the temperature is (a) \(90^\circ C\), (b)\(-20^\circ C\)?

Problem 10P To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter at 20°C. To what temperature must the rivet be cooled if it is to fit in the hole?

A flat, uniform cylinder of lead floats in mercury at \(0^{\circ} \mathrm{C}\). Will the lead float higher or lower when the temperature is raised? Explain.

Problem 11P The density of water at 4°C is 1.00 × 103kg/m3. What is water’s density at 94°C?

When a cold mercury-in-glass thermometer is first placed in a hot tub of water, the mercury initially descends a bit and then rises. Explain.

Problem 72P (II) Oxygen diffuses from the surface of insects to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectional area of 2X 10-9 m2 Assuming the concentration of oxygen inside is half what it is outside in the atmosphere, (a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20°C is about 8.7 mol/m3 then (b) calculate the diffusion rate J, and (c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is 1X 10-5 m2/s.

A quartz sphere is \(8.75 \mathrm{~cm}\) in diameter. What will be its change in volume if it is heated from \(30^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\)?

Problem 13P An ordinary glass is filled to the brim with 350.0 mL of water at 100.0°C. If the temperature decreased to 20.0°C, how much water could be added to the glass?

Problem 77GP In outer space the density of matter is about one atom per cm3 mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).

Problem 14Q Will a grandfather clock, accurate at 20°C, run fast or slow on a hot day (30°C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

The lowest pressure attainable using the best available vacuum techniques is about \(10^{-12} \ \mathrm {N/m}^2\). At such a pressure, how many molecules are there per \(\mathrm {cm}^3\) at \(0^\circ{C}\)?

Problem 15P (a) A brass plug is to be placed in a ring made of iron. At 20°C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit? (b) What if the plug were iron and the ring brass?

Problem 16P If a fluid is contained in a long, narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion ? is approximately equal to the coefficient of volume expansion ?.

Problem 16Q When a gas is rapidly compressed (say, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Problem 17P (a) Show that the change in the density ? of a substance, when the temperature changes by ?T, is given by ? ? = ? ? ? ?T. (b) What is the fractional change in density of a lead sphere whose temperature decreases from 25°C to ?40°C?

(II) A uniform rectangular plate of length l and width w has coefficient of linear expansion \(\alpha\). Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change \(\Delta T \text { is } \Delta A=2 \alpha l w \Delta T\). See Fig. 13–30. Equation Transcription: Text Transcription: \alpha \Delta T is \Delta A=2 \alpha l w \Delta T

Explain in words how Charles’s law follows from kinetic theory and the relation between average kinetic energy and the absolute temperature.

(III) Show that for an isotropic solid, \(\beta=3 \alpha \), if the amount of expansion is small. \(\beta \text { and } \alpha\) are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.] Equation Transcription: Text Transcription: \beta=3 \alpha \beta and \alpha

Problem 19Q Explain in words how Gay-Lussac’s law follows from kinetic theory.

Problem 20P The pendulum in a grandfather clock is made of brass and keeps perfect time at 17°C. How much time is gained or lost in a year if the clock is kept at 25°C? (Assume the frequency dependence on length for a simple pendulum applies.)

Problem 20Q As you go higher in the Earth’s atmosphere, the ratio of N2 molecules to O2 molecules increases. Why?

Problem 89GP A brass lid screws tightly onto a glass jar at 20°C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60°C. The inside diameter of the lid is 8.0 cm at 20°C. Find the size of the gap (difference in radius) that develops by this procedure.

Problem 21Q Escape velocity for the Earth refers to the minimum speed an object must have to leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Problem 92GP The escape speed from the Earth is 1.12*104 m/s, so that a gas molecule traveling away from Earth near the outer boundary of the Earth's atmosphere would, at this speed, be able to escape from the Earth's gravitational field and be lost to the atmosphere. At what temperature is the rms speed of (a) oxygen molecules, and (b) helium atoms equal to1.12*104 m/s? (c) Can you explain why our atmosphere contains oxygen but not helium?

Alcohol evaporates more quickly than water at room temperature. What can you infer about the molecular properties of one relative to the other?

Explain why a hot humid day is far more uncomfortable than a hot dry day at the same temperature.

(III) A barrel of diameter \(134.122 \mathrm{~cm}\) at \(20^{\circ} \mathrm{C}\) is to be enclosed by an iron band. The circular band has an inside diameter of \(134.110 \mathrm{~cm}\) at \(20^{\circ} \mathrm{C}\). It is \(7.4 \mathrm{~cm}\) wide and \(0.65 \mathrm{~cm}\) thick. (a) To what temperature must the band be heated so that it will fit over the barrel? (b) What will be the tension in the band when it cools to \(20^{\circ} \mathrm{C}\)?

Problem 25Q Consider two days when the air temperature is the same but the humidity is different. Which is more dense, the dry air or the humid air at the same T? Explain.

Problem 33P A storage tank at STP contains 18.5 kg of nitrogen (N2). (a) What is the volume of the tank? (b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?

If 61.5 L of oxygen at \(18.0 ^\circ \ {C}\) and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to \(50.0^\circ \ {C}\), what will the new pressure be?

(III) A helium-filled balloon escapes a child's hand at sea level and \(20.0^{\circ} \mathrm{C}\). When it reaches an altitude of \(3000 \mathrm{~m}\), where the temperature is \(5.0^{\circ} \mathrm{C}\) and the pressure is only \(0.70 \mathrm{~atm}\), how will its volume compare to that at sea level?

How many moles of water are there in 1.000 L? How many molecules?

Problem 44P A cubic box of volume 5.1 × 10?2 m3 is filled with air at atmospheric pressure at 20°C. The box is closed and heated to 180°C. What is the net force on each side of the box?

Problem 45P Estimate how many molecules of air are in each 2.0-L breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]

(I) (a) What is the average translational kinetic energy of an oxygen molecule at STP? (b) What is the total translational kinetic energy of 2.0 mol of \(O_2\) molecules at \(20^\circ{C}\)?

(I) By what factor will the rms speed of gas molecules increase if the temperature is increased from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\) ?

(I) Twelve molecules have the following speeds, given in units of km/s: 6, 2, 4, 6, 0, 4,1, 8, 5, 3, 7, and 8. Calculate the rms speed.

Problem 51P The rms speed of molecules in a gas at 20.0°C is to be increased by 1.0%. To what temperature must it be raised?

Problem 52P If the pressure of a gas is doubled while its volume is held constant, by what factor does vrmschange?

Problem 54P Show that for a mixture of two gases at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of their molecular masses.

Problem 55P What is the rms speed of nitrogen molecules contained in an 8.5-m3 volume at 2.1 atm if the total amount of nitrogen is 1300 mol?

Problem 56P Calculate (a) the rms speed of an oxygen molecule at 0°C and (b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.

(II) What is the average distance between nitrogen molecules at STP?

Problem 58P (a) Estimate the rms speed of an amino acid whose molecular mass is 89 u in a living cell at 37°C. (b) What would be the rms speed of a protein of molecular mass 50,000 u at 37°C?

Show that the pressure P of a gas can be written \(P=\frac{1}{3} p v^{2}\), where ? is the density of the gas and v is the rms speed of the molecules. Equation Transcription: Text Transcription: P=\frac{1}{3} p v^2

Problem 63P What is the dew point (approximately) if the humidity is 50% on a day when the temperature is 25°C?

Problem 64P What is the air pressure at a place where water boils at 90°C?

Problem 65P If the air pressure at a particular place in the mountains is 0.72 atm, estimate the temperature at which water boils.

Problem 66P What is the temperature on a day when the partial pressure of water is 530 Pa and the relative humidity is 40%?

Problem 67P What is the partial pressure of water on a day when the temperature is 25°C and the relative humidity is 35%?

Problem 68P What is the approximate pressure inside a pressure cooker if the water is boiling at a temperature of 120°C? Assume no air escaped during the heating process, which started at 20° C.

Problem 69P If the humidity in a room of volume 680 m3 at 25°C is 80%, what mass of water can still evaporate from an open pan?

Problem 70P Air that is at its dew point of 5°C is drawn into a building where it is heated to 25°C. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.

(II) Estimate the time needed for a glycine molecule (see Table 13–4) to diffuse a distance of \(\mu m\) in water at 20°C if its concentration varies over that distance from \(1.00 \mathrm{~mol} / \mathrm{m}^{3} \text { to } 0.40 \mathrm{~mol} / \mathrm{m}^{3}\). Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. Equation Transcription: Text Transcription: \mu m 1.00 mol/m3 to 0.40 mol/m3

A precise steel tape measure has been calibrated at \(20^\circ {C}\). At \(34^\circ {C}\), (a) will it read high or low, and (b) what will be the percentage error?

Problem 75GP The gauge pressure in a helium gas cylinder is initially 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 300 mL of cool water, if the water and the cup are hot, at \(80^\circ {C}\), instead of at \(20^\circ {C}\)? Neglect the glass expansion.

Problem 76GP Estimate the number of air molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume the temperature is 22°C. How many moles does that correspond to?

If a scuba diver fills his lungs to full capacity of 5.5 L when 10 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

A space vehicle returning from the Moon enters Earth’s atmosphere at a speed of about 40,000 km/h. Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)

Problem 81GP The temperature of an ideal gas is increased from 110°C to 360°C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor docs vrms change?

Problem 82GP A house has a volume of 770 m3. (a) What is the total mass of air inside the house at 20°C? (b) If the temperature drops to ?10°C, what mass of air enters or leaves the house?

Problem 83GP From the known value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth’s atmosphere.

Problem 84GP What is the rms speed of nitrogen molecules contained in a 7.6-m3 volume at 4.2 atm if the total amount of nitrogen is 1800 mol?

A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and \(\mathrm {volume = 16 \ L (0.016 \ m}^3)\) at T = 295 K. How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min?

Problem 86GP An iron cube floats in a bowl of liquid mercury at 0°C. (a) If the temperature is raised to 25°C, will the cube float higher or lower in the mercury? (b) By what percent will the fraction of volume submerged change?

Problem 87GP The density of gasoline at 0°C is 0.68 × 103kg/m3. What is the density on a hot day, when the temperature is 38°C? What is the percentage change?

If a steel band were to fit snugly around the Earth's equator at \(25^{\circ} \mathrm{C}\), but then was heated to \(45^{\circ} \mathrm{C}\), how high above the Earth would the band be (assume equal everywhere)?

Problem 90GP The first length standard, adopted in the 18th century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within ±1.0 ?m, how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is 9 × 10?6 C°?1.

A scuba tank, when fully charged, has a pressure of \(195 \mathrm{~atm}\) at \(20^{\circ} \mathrm{C}\). The volume of the tank is \(11.3 \mathrm{~L}\). (a) What would the volume of the air be at \(1.00 \mathrm{~atm}\) and at the same temperature? (b) Before entering the water, a person consumes \(2.0 \mathrm{~L}\) of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last? (c) At a depth of \(20.0 \mathrm{~m}\) of sea water and temperature of \(10^{\circ} \mathrm{C}\), how long would the same tank last assuming the breathing rate does not change?

Problem 93GP A 1.0-kg trash-can lid is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12 m/s?

A scuba diver releases a 3.00-cm-diameter (spherical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surface?

Problem 95GP Calculate the total water vapor pressure in the air on the following two days: (a) a hot summer day, with the temperature 30°C and the relative humidity at 40%; (b) a cold winter day, with the temperature 5°C and the relative humidity at 80%.

A sauna has \(7.0 \mathrm{~m}^{3}\) of air volume, and the temperature is 90°C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.) Equation Transcription: Text Transcription: 7.0 m^3

Estimate the percent difference in the density of iron at STP, and when it is a solid deep in the Earth where the temperature is \(2000^\circ {C}\) and under 5000 atm of pressure. Assume the bulk modulus \((90 \times 10^9 \ \mathrm {N/m^2})\) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.

(a) Use the ideal gas law to show that, for an ideal gas at constant pressure, the coefficient of volume expansion is equal to \(\beta=1 / T\), where T is the temperature in Kelvins. Compare to Table 13–1 for gases at T = 293 K. (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P, where P is the pressure. Equation Transcription: Text Transcription: \beta=1 / T

In humid climates, people constantly dehumidify their cellars to prevent rot and mildew. If the cellar in a house (kept at \(20^{\circ} \mathrm{C}\) ) has \(95 \mathrm{~m}^2\) of floor space and a ceiling height of \(2.8 \mathrm{~m}\), what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30% ?