College Physics for AP® Courses

# Problems & Exercises

### 13.1Temperature

1.

What is the Fahrenheit temperature of a person with a $39.0ºC39.0ºC size 12{"39" "." 0°C} {}$ fever?

2.

Frost damage to most plants occurs at temperatures of $28.0ºF28.0ºF size 12{"28" "." 0°F} {}$ or lower. What is this temperature on the Kelvin scale?

3.

To conserve energy, room temperatures are kept at $68.0ºF68.0ºF size 12{"68" "." 0°F} {}$ in the winter and $78.0ºF78.0ºF size 12{"78" "." 0°F} {}$ in the summer. What are these temperatures on the Celsius scale?

4.

A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?

5.

The surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?

6.

One of the hottest temperatures ever recorded on the surface of Earth was $134ºF134ºF size 12{"134"°F} {}$ in Death Valley, CA. What is this temperature in Celsius degrees? What is this temperature in Kelvin?

7.

(a) Suppose a cold front blows into your locale and drops the temperature by 40.0 Fahrenheit degrees. How many degrees Celsius does the temperature decrease when there is a $40.0ºF40.0ºF size 12{"40" "." 0°F} {}$ decrease in temperature? (b) Show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees.

8.

(a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value? (b) At what temperature do the Fahrenheit and Kelvin scales have the same numerical value?

### 13.2Thermal Expansion of Solids and Liquids

9.

The height of the Washington Monument is measured to be 170 m on a day when the temperature is $35.0ºC35.0ºC size 12{"35" "." 0°C} {}$. What will its height be on a day when the temperature falls to $–10.0ºC–10.0ºC size 12{–"10" "." 0°C} {}$? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

10.

How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by $15ºC15ºC size 12{"15"°C} {}$? Its original height is 321 m and you can assume it is made of steel.

11.

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from $37.0ºC37.0ºC size 12{"37" "." 0°C} {}$ to $40.0ºC40.0ºC size 12{"40" "." 0°C} {}$, assuming the mercury is unconstrained?

12.

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature $35.0ºC35.0ºC size 12{"35" "." 0°C} {}$ greater than when they were laid? Their original length is 10.0 m.

13.

You are looking to purchase a small piece of land in Hong Kong. The price is “only” \$60,000 per square meter! The land title says the dimensions are $20 m ×30 m.20 m ×30 m. size 12{"20"" m " times "30 m" "." } {}$ By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was $20ºC20ºC size 12{"20"°C} {}$ above normal?

14.

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of $1.00ºC.1.00ºC. size 12{1 "." "00"°C "." } {}$ Note that this calculation is only approximate because ocean warming is not uniform with depth.

15.

Show that 60.0 L of gasoline originally at $15.0ºC15.0ºC size 12{"15" "." 0°C} {}$ will expand to 61.1 L when it warms to $35.0ºC,35.0ºC, size 12{"35" "." 0°"C,"} {}$ as claimed in Example 13.4.

16.

(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at $0ºC0ºC size 12{0°C} {}$. What is their difference in length at $22.0ºC22.0ºC size 12{"22" "." 0°C} {}$? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

17.

(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of $5.00ºC,5.00ºC, size 12{5 "." "00"°"C,"} {}$ how much will overflow when its temperature reaches $22.0ºC22.0ºC size 12{"22" "." 0°C} {}$? (b) How much less water would overflow under the same conditions?

18.

Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at $10.0ºC.10.0ºC. size 12{"10" "." 0°C "." } {}$ What volume of radiator fluid will overflow when the radiator and fluid reach their $95.0ºC95.0ºC size 12{"95" "." 0°C} {}$ operating temperature, given that the fluid’s volume coefficient of expansion is $β=400×10–6/ºCβ=400×10–6/ºC size 12{β="400"´"10" rSup { size 8{ +- 6} } /°C} {}$? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than $95.0ºC.95.0ºC. size 12{"95" "." 0°C "." } {}$

19.

A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the $350 cm3350 cm3 size 12{"350"" cm" rSup { size 8{3} } } {}$ of coffee is in a 7.00-cm-diameter cup and decreases in temperature from $95.0ºC95.0ºC size 12{"95" "." 0°C} {}$to$45.0ºC.45.0ºC. size 12{"45" "." 0°C "." } {}$ (Most of the drop in level is actually due to escaping bubbles of air.)

20.

(a) The density of water at $0ºC0ºC size 12{0°C} {}$ is very nearly $1000 kg/m31000 kg/m3 size 12{"1000"" kg/m" rSup { size 8{3} } } {}$ (it is actually $999.84 kg/m3999.84 kg/m3 size 12{9"99" "." "84 kg/m" rSup { size 8{3} } } {}$), whereas the density of ice at $0ºC0ºC size 12{0°C} {}$ is $917 kg/m3917 kg/m3 size 12{9"17 kg/m" rSup { size 8{3} } } {}$. Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.) (b) What are the implications of this result for biological cells that are frozen?

21.

Show that $β≈3α,β≈3α, size 12{β»3α,} {}$ by calculating the change in volume $ΔVΔV size 12{ΔV} {}$ of a cube with sides of length $L.L. size 12{L "." } {}$

### 13.3The Ideal Gas Law

22.

The gauge pressure in your car tires is $2.50×105 N/m22.50×105 N/m2 size 12{2 "." "50"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {}$ at a temperature of $35.0ºC35.0ºC size 12{"35" "." 0°C} {}$ when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to $–40.0ºC–40.0ºC size 12{ +- "40" "." 0°C} {}$?

23.

Convert an absolute pressure of $7.00×105 N/m27.00×105 N/m2 size 12{7 "." "00" times "10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {}$ to gauge pressure in $lb/in2.lb/in2. size 12{"lb/in" rSup { size 8{2} } "." } {}$ (This value was stated to be just less than $90.0 lb/in290.0 lb/in2 size 12{"90" "." "0 lb/in" rSup { size 8{2} } } {}$ in Example 13.9. Is it?)

24.

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $60.0ºC60.0ºC size 12{"60" "." 0°C} {}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?

25.

Large helium-filled balloons are used to lift scientific equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of $10.0ºC10.0ºC size 12{"10" "." 0°C} {}$ and rises to an altitude where its volume is twenty times the original volume and its temperature is $–50.0ºC–50.0ºC size 12{ +- "50" "." 0°C} {}$? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)

26.

Confirm that the units of $nRTnRT size 12{ ital "nRT"} {}$ are those of energy for each value of $RR size 12{R} {}$: (a) $8.31 J/mol⋅K8.31 J/mol⋅K size 12{8 "." "31"" J/mol" cdot K} {}$, (b) $1.99 cal/mol⋅K1.99 cal/mol⋅K size 12{1 "." "99 cal/mol" cdot K} {}$, and (c) $0.0821 L⋅atm/mol⋅K0.0821 L⋅atm/mol⋅K size 12{0 "." "0821 L" cdot "atm/mol" cdot K} {}$.

27.

In the text, it was shown that $N/V=2.68×1025m−3N/V=2.68×1025m−3 size 12{N/V=2 "." "68" times "10" rSup { size 8{"25"} } m rSup { size 8{ - 3} } } {}$ for gas at STP. (a) Show that this quantity is equivalent to $N/V=2.68×1019cm−3,N/V=2.68×1019cm−3, size 12{N/V=2 "." "68" times "10" rSup { size 8{"19"} } "cm" rSup { size 8{ - 3} } ,} {}$ as stated. (b) About how many atoms are there in one $μm3μm3 size 12{"μm" rSup { size 8{3} } } {}$ (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of atoms and molecules?

28.

Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person. Note that the air is at $37.0ºC37.0ºC size 12{"37" "." 0°C} {}$ (body temperature).

29.

An airplane passenger has $100 cm3100 cm3 size 12{"100"" cm" rSup { size 8{3} } } {}$ of air in his stomach just before the plane takes off from a sea-level airport. What volume will the air have at cruising altitude if cabin pressure drops to $7.50×104 N/m2?7.50×104 N/m2? size 12{7 "." "50"´"10" rSup { size 8{4} } " N/m" rSup { size 8{2} } } {}$

30.

(a) What is the volume (in $km3km3 size 12{"km" rSup { size 8{3} } } {}$) of Avogadro’s number of sand grains if each grain is a cube and has sides that are 1.0 mm long? (b) How many kilometers of beaches in length would this cover if the beach averages 100 m in width and 10.0 m in depth? Neglect air spaces between grains.

31.

An expensive vacuum system can achieve a pressure as low as $1.00×10–7 N/m21.00×10–7 N/m2 size 12{1 "." "00"´"10" rSup { size 8{ +- 7} } " N/m" rSup { size 8{2} } } {}$ at $20ºC20ºC size 12{"20"°C} {}$. How many atoms are there in a cubic centimeter at this pressure and temperature?

32.

The number density of gas atoms at a certain location in the space above our planet is about $1.00×1011m−3,1.00×1011m−3, size 12{1 "." "00" times "10" rSup { size 8{"11"} } m rSup { size 8{ - 3} } ,} {}$ and the pressure is $2.75×10–10 N/m22.75×10–10 N/m2 size 12{2 "." "75"´"10" rSup { size 8{ +- "10"} } " N/m" rSup { size 8{2} } } {}$ in this space. What is the temperature there?

33.

A bicycle tire has a pressure of $7.00×105 N/m27.00×105 N/m2 size 12{7 "." "00"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {}$ at a temperature of $18.0ºC18.0ºC size 12{"18" "." 0°C} {}$ and contains 2.00 L of gas. What will its pressure be if you let out an amount of air that has a volume of $100 cm3100 cm3 size 12{"100"" cm" rSup { size 8{3} } } {}$ at atmospheric pressure? Assume tire temperature and volume remain constant.

34.

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1.40×107 N/m21.40×107 N/m2 size 12{1 "." "40"´"10" rSup { size 8{7} } " N/m" rSup { size 8{2} } } {}$ and a temperature of $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature $(–78.5ºC)(–78.5ºC) size 12{ $$–"78" "." 5°C$$ } {}$ to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

35.

Find the number of moles in 2.00 L of gas at $35.0ºC35.0ºC size 12{"35" "." 0°C} {}$ and under $7.41×107 N/m27.41×107 N/m2 size 12{7 "." "41"´"10" rSup { size 8{7} } " N/m" rSup { size 8{2} } } {}$ of pressure.

36.

Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.

37.

(a) What is the gauge pressure in a $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$ car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$? Assume the temperature returns to $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$ and the volume remains constant.

38.

(a) In the deep space between galaxies, the density of atoms is as low as $106 atoms/m3,106 atoms/m3, size 12{"10" rSup { size 8{6} } " atoms/m" rSup { size 8{3} } ,} {}$ and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in $m3m3 size 12{m rSup { size 8{3} } } {}$) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?

### 13.4Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

39.

Some incandescent light bulbs are filled with argon gas. What is $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ for argon atoms near the filament, assuming their temperature is 2500 K?

40.

Average atomic and molecular speeds $(vrms)(vrms) size 12{ $$v rSub { size 8{"rms"} }$$ } {}$ are large, even at low temperatures. What is $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ for helium atoms at 5.00 K, just one degree above helium’s liquefaction temperature?

41.

(a) What is the average kinetic energy in joules of hydrogen atoms on the $5500ºC5500ºC size 12{"5500"°C} {}$ surface of the Sun? (b) What is the average kinetic energy of helium atoms in a region of the solar corona where the temperature is $6.00×105K6.00×105K size 12{6 "." "00"´"10" rSup { size 8{5} } " K"} {}$?

42.

The escape velocity of any object from Earth is 11.2 km/s. (a) Express this speed in m/s and km/h. (b) At what temperature would oxygen molecules (molecular mass is equal to 32.0 g/mol) have an average velocity $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ equal to Earth’s escape velocity of 11.1 km/s?

43.

The escape velocity from the Moon is much smaller than from Earth and is only 2.38 km/s. At what temperature would hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ equal to the Moon’s escape velocity?

44.

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of $6.40×10–14J6.40×10–14J size 12{6 "." "40"´"10" rSup { size 8{ +- "14"} } " J"} {}$. What temperature is needed?

45.

Suppose that the average velocity $(vrms)(vrms) size 12{ $$v rSub { size 8{"rms"} }$$ } {}$ of carbon dioxide molecules (molecular mass is equal to 44.0 g/mol) in a flame is found to be $1.05×105m/s1.05×105m/s size 12{1 "." "05"´"10" rSup { size 8{5} } " m/s"} {}$. What temperature does this represent?

46.

Hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ equal to 193 m/s. What is the temperature?

47.

Much of the gas near the Sun is atomic hydrogen. Its temperature would have to be $1.5×107K1.5×107K size 12{1 "." 5´"10" rSup { size 8{7} } " K"} {}$ for the average velocity $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ to equal the escape velocity from the Sun. What is that velocity?

48.

There are two important isotopes of uranium— $235U235U size 12{ {} rSup { size 8{"235"} } U} {}$ and $238U238U size 12{ {} rSup { size 8{"238"} } U} {}$; these isotopes are nearly identical chemically but have different atomic masses. Only $235U235U size 12{ {} rSup { size 8{"235"} } U} {}$ is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ of uranium hexafluoride gas, $UF6UF6 size 12{"UF" rSub { size 8{6} } } {}$. (a) The molecular masses for $235U235U size 12{ {} rSup { size 8{"235"} } U} {}$$UF6UF6 size 12{"UF" rSub { size 8{6} } } {}$ and $238U238U size 12{ {} rSup { size 8{"238"} } U} {}$$UF6UF6 size 12{"UF" rSub { size 8{6} } } {}$ are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities? (b) At what temperature would their average velocities differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?

### 13.6Humidity, Evaporation, and Boiling

49.

Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is $1.01×105 N/m21.01×105 N/m2 size 12{1 "." "01"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {}$?

50.

(a) What is the vapor pressure of water at $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$? (b) What percentage of atmospheric pressure does this correspond to? (c) What percent of $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$ air is water vapor if it has 100% relative humidity? (The density of dry air at $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$ is $1.20 kg/m31.20 kg/m3 size 12{1 "." "20"" kg/m" rSup { size 8{3} } } {}$.)

51.

Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to $120.0ºC120.0ºC size 12{"120" "." 0°C} {}$? (b) What gauge pressure does this correspond to?

52.

(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is $8.59×104 N/m2?8.59×104 N/m2? size 12{8 "." "59" times "10" rSup { size 8{4} } " N/m" rSup { size 8{2} } ?} {}$ (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is $7.00×104 N/m2?7.00×104 N/m2? size 12{7 "." "00" times "10" rSup { size 8{4} } " N/m" rSup { size 8{2} } ?} {}$

53.

What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of $70.0ºC?70.0ºC? size 12{"70" "." 0°"C?"} {}$

54.

At a spot in the high Andes, water boils at $80.0ºC80.0ºC size 12{"80" "." 0°C} {}$, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location?

55.

What is the relative humidity on a $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$ day when the air contains $18.0 g/m318.0 g/m3 size 12{"18" "." 0" g/m" rSup { size 8{3} } } {}$ of water vapor?

56.

What is the density of water vapor in $g/m3g/m3 size 12{"g/m" rSup { size 8{3} } } {}$ on a hot dry day in the desert when the temperature is $40.0ºC40.0ºC size 12{"40" "." 0°C} {}$ and the relative humidity is 6.00%?

57.

A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of $1.01×105 N/m21.01×105 N/m2 size 12{1 "." "01"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {}$. (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of $2.00×106 N/m22.00×106 N/m2 size 12{2 "." "00"´"10" rSup { size 8{6} } " N/m" rSup { size 8{2} } } {}$, what percent oxygen should it be to have the same oxygen partial pressure as at sea level?

58.

The vapor pressure of water at $40.0ºC40.0ºC size 12{"40" "." 0°C} {}$ is $7.34×103 N/m27.34×103 N/m2 size 12{7 "." "34"´"10" rSup { size 8{3} } " N/m" rSup { size 8{2} } } {}$. Using the ideal gas law, calculate the density of water vapor in $g/m3g/m3 size 12{"g/m" rSup { size 8{3} } } {}$ that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature $(51.1 g/m3).(51.1 g/m3). size 12{ $$"51" "." "1 g/m" rSup { size 8{3} }$$ "." } {}$

59.

Air in human lungs has a temperature of $37.0ºC37.0ºC size 12{"37" "." 0°C} {}$ and a saturation vapor density of $44.0 g/m344.0 g/m3 size 12{"44" "." "0 g/m" rSup { size 8{3} } } {}$. (a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person? (b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of $6.31×103 N/m26.31×103 N/m2 size 12{6 "." "31"´"10" rSup { size 8{3} } " N/m" rSup { size 8{2} } } {}$.

60.

If the relative humidity is 90.0% on a muggy summer morning when the temperature is $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$, what will it be later in the day when the temperature is $30.0ºC30.0ºC size 12{"30" "." 0°C} {}$, assuming the water vapor density remains constant?

61.

Late on an autumn day, the relative humidity is 45.0% and the temperature is $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$. What will the relative humidity be that evening when the temperature has dropped to $10.0ºC10.0ºC size 12{"10" "." 0°C} {}$, assuming constant water vapor density?

62.

Atmospheric pressure atop Mt. Everest is $3.30 × 104 N/m23.30 × 104 N/m2 size 12{3 "." "30"´"10" rSup { size 8{4} } " N/m" rSup { size 8{2} } } {}$. (a) What is the partial pressure of oxygen there if it is 20.9% of the air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is $1.01×105 N/m2?1.01×105 N/m2? size 12{1 "." "01" times "10" rSup { size 8{5} } " N/m" rSup { size 8{2} } ?} {}$ (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur?

63.

What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of $20.0ºC20.0ºC size 12{"20" "." 0°C} {}$?

64.

On a certain day, the temperature is $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$ and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to $15.0ºC15.0ºC size 12{"15" "." 0°C} {}$? Such a drop in temperature can, thus, produce heavy dew or fog.

65.

Integrated Concepts

The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of $150ºC150ºC size 12{"150"°C} {}$, if the surface of the water is at sea level?

66.

Integrated Concepts

(a) At what depth in fresh water is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth?

67.

Integrated Concepts

To get an idea of the small effect that temperature has on Archimedes’ principle, calculate the fraction of a copper block’s weight that is supported by the buoyant force in $0ºC0ºC size 12{0°C} {}$ water and compare this fraction with the fraction supported in $95.0ºC95.0ºC size 12{"95" "." 0°C} {}$ water.

68.

Integrated Concepts

If you want to cook in water at $150ºC150ºC size 12{"150"°C} {}$, you need a pressure cooker that can withstand the necessary pressure. (a) What pressure is required for the boiling point of water to be this high? (b) If the lid of the pressure cooker is a disk 25.0 cm in diameter, what force must it be able to withstand at this pressure?

69.

Unreasonable Results

(a) How many moles per cubic meter of an ideal gas are there at a pressure of $1.00×1014 N/m21.00×1014 N/m2 size 12{1 "." "00"´"10" rSup { size 8{"14"} } " N/m" rSup { size 8{2} } } {}$ and at $0ºC0ºC size 12{0°C} {}$? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

70.

Unreasonable Results

(a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If the hole is 10.0% bigger in diameter than the $22.0ºC22.0ºC size 12{"22" "." 0°C} {}$ rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (c) Which premise is responsible?

71.

Unreasonable Results

The temperature inside a supernova explosion is said to be $2.00×1013 K2.00×1013 K size 12{2 "." "00"´"10" rSup { size 8{"13"} } " K"} {}$. (a) What would the average velocity $vrmsvrms size 12{v rSub { size 8{"rms"} } } {}$ of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?

72.

Unreasonable Results

Suppose the relative humidity is 80% on a day when the temperature is $30.0ºC30.0ºC size 12{"30" "." 0°C} {}$. (a) What will the relative humidity be if the air cools to $25.0ºC25.0ºC size 12{"25" "." 0°C} {}$ and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?