Solved: The quantity of heat Q that changes the

Problem 1E Alcohol evaporates more quickly than water at the same temperature. Which produces more cooling—alcohol or the same amount of water on your skin?

Problem 1P The quantity of heat Q that changes the temperature ?T of a mass m of a substance is given by Q = cm?T, where c is the specific heat capacity of the substance. For example, for H2O, c = 1 cal/g°C. And for a change of phase, the quantity of heat Q that changes the phase of a massm is Q = mL, where L is the heat of fusion or heat of vaporization of the substance. For example, for H2O, the heat of fusion is 80 cal/g (or 80 kcal/kg) and the heat of vaporization is 540 cal/g (or 540 kcal/kg). Use these relationships to determine the number of calories to change (a) 1 kg of 0°C ice to 0°C ice water, (b) 1 kg of 0°C ice water to 1 kg of 100°C boiling water, (c) 1 kg of 100°C boiling water to 1 kg of 100°C steam, and (d) 1 kg of 0°C ice to 1 kg of 100°C steam.

What are the four common phases of matter?

Problem 2E You can determine wind direction by wetting your finger and holding it up in the air. Explain.

Problem 2P The specific heat capacity of ice is about 0.5 cal/g°C. Supposing that it remains at that value all the way to absolute zero, calculate the number of calories it would take to change a 1-g ice cube at absolute zero (?273°C) to 1 g of boiling water. How does this number of calories compare with the number of calories required to change the same gram of 100°C boiling water to 100°C steam?

Problem 2RQ Do the molecules in a liquid all have about the same speed, or do they have a wide variety of speeds?

Problem 3E When you step out of a swimming pool on a hot, dry day in the Southwest, you feel quite chilly. Why?

Problem 3P Find the mass of 0°C ice that 10 g of 100°C steam will completely melt.

Problem 3RQ What is evaporation, and why is it a cooling process? Exactly what is it that cools?

Problem 4E Why is sweating an efficient mechanism for cooling off on a hot day?

Problem 4P Consider 50 g of hot water at 80°C poured into a cavity in a very large block of ice at 0°C. What will be the final temperature of the water in the cavity? Show that 50 g of ice must melt in order to cool the hot water down to this temperature.

Problem 4RQ Why does warmer water evaporate more readily than cold water?

Why does blowing over hot soup cool the soup?

Problem 5P A 50-g chunk of 80°C iron is dropped into a cavity in a very large block of ice at 0°C. Show that 5.5 g of ice will melt. (The specific heat capacity of iron is 0.11 cal/g°C.)

Problem 5RQ What is sublimation?

Problem 6E Can you give two reasons why pouring a cup of hot coffee into a saucer results in faster cooling?

Problem 6P If you drop a piece of ice on a hard surface, the energy of impact will melt some of the ice. The higher it drops, the more ice will melt upon impact. Show that to completely melt a block of ice that falls without air drag, it should ideally be dropped from a height of 34 km. [Hint: Equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (in SI units, 335,000 J/kg). Do you see why the answer doesn’t depend on mass?]

Problem 6RQ Distinguish between condensation and evaporation.

Problem 7E What happens to the temperature of a pan of water when evaporation exceeds condensation?

Problem 7P A 10-kg iron ball is dropped onto a pavement from a height of 100 m. If half of the heat generated goes into 3 warming the ball, find the temperature increase of the ball. (In SI units, the specific heat capacity of iron is 450 J/kg°C.) Why is the answer the same for a ball of any mass?

Problem 7RQ Why is a steam burn more damaging than a burn from boiling water of the same temperature?

What is the source of energy that keeps the dunking bird in Figure 17.4 operating?

Problem 8P The heat of vaporization of ethyl alcohol is about 200 cal/g. If 2 kg of this fluid were allowed to vaporize in a refrigerator, show that 5 kg of ice would be formed from 0°C water.

Problem 8RQ Why do you feel uncomfortably warm on a hot and humid day?

Problem 9E An inventor claims to have developed a new perfume that lasts a long time because it doesn’t evaporate. Comment on this claim.

Problem 10E Pretend that all the molecules in a liquid have the same speed, not random speeds. Would evaporation of this liquid cause the remaining liquid to be cooled? Explain.

Problem 10RQ Why does water vapor in the air condense when the air is chilled?

Problem 11E Does a common electric fan cool the air in a room? If not, then why is it used in an overly warm room?

Problem 11RQ Why does warm, moist air form clouds when it rises?

Problem 12E Porous canvas bags filled with water are used by travelers in hot weather. When the bags are slung on the outside of a fast-moving car, the water inside is cooled considerably. Explain.

Problem 12RQ What is the basic difference between a cloud and fog?

Problem 13E Why will wrapping a bottle in a wet cloth at a picnic often produce a cooler bottle than placing the bottle in a bucket of cold water?

Problem 13RQ Distinguish between evaporation and boiling.

Problem 14E The human body can maintain its customary temperature of 37°C on a day when the temperature is above 40°C. How is this done?

Double-pane windows have nitrogen gas or very dry air between the panes. Why is ordinary air a poor idea?

Problem 14RQ Does increased atmospheric pressure increase or decrease the boiling point of water? Why is this so?

Problem 15RQ Double-pane windows have nitrogen gas or very dry air between the panes. Why is ordinary air a poor idea?

Problem 16E Why are icebergs often surrounded by fog?

Problem 16RQ Why will water at the bottom of a geyser not boil when it is at 100°C?

Problem 17E How does Figure 17.7 help explain the moisture that forms on the inside of car windows when you’re parking with your date on a cool night?

What happens to the water pressure at the bottom of a geyser when some of the water above gushes out?

Problem 18E You know that the windows in your warm house get wet on a cold day. But can moisture form on the windows if the interior of your house is cold on a hot day? How is this different?

Problem 18RQ The temperature of boiling water doesn’t increase with continued energy input. Why is this evidence that boiling is a cooling process?

Problem 19E On freezing days, frost often forms on windows. Why is there usually more frost on the bottom portions of the windows?

Problem 19RQ When will water boil at a temperature of less than 100°C?

Problem 20E Why do clouds often form above mountain peaks? (Hint: Consider the updrafts.)

Problem 20RQ What evidence can you cite for the claim that water can boil at a temperature of 0°C?

Problem 21E Why will clouds tend to form above either a flat or a mountainous island in the middle of the ocean? (Hint: Compare the specific heat capacity of the land with that of the water and the subsequent convection currents in the air.)

Problem 21RQ Why does increasing the temperature of a solid make it melt?

Problem 22E A great amount of water vapor changes phase to become water in the clouds that form a thunderstorm. Does this release thermal energy or absorb it?

Problem 22RQ Why does decreasing the temperature of a liquid make it freeze?

Problem 23E When can you add heat to something without raising its temperature?

Problem 23RQ Why does freezing of water not occur at 0°C when foreign ions are present?

Problem 24E When can you withdraw heat from something without lowering its temperature?

Problem 24RQ What happens to the hexagonal open structure of ice when sufficient pressure is applied to it?

Problem 25E Why does the temperature of boiling water remain the same as long as the heating and boiling continue?

Problem 25RQ Why does a wire not simply cut a block of ice in two when it passes through the ice?

Problem 26E Why do vapor bubbles in a pot of boiling water increase in size as they rise in the water?

Does a liquid release energy or absorb energy when it changes into a gas?

Problem 27E Why does the boiling temperature of water decrease when the water is under reduced pressure, such as when it is at a higher altitude?

Problem 27RQ Does a liquid release energy or absorb energy when it changes into a solid?

Problem 28E Place a jar of water on a small stand within a saucepan of water so that the bottom of the jar is held above the bottom of the pan. When the pan is placed on a stove, the water in the pan will boil, but not the water in the jar. Why?

Problem 28RQ Is heat discharged at the back of a refrigerator and by a heat pump given off by vaporization of the refrigerating fluid or by condensation?

Hydrothermal vents are openings in the ocean floor that discharge very hot water. Water emerging at nearly \(280^{\circ} \mathrm{C}\) from one such vent off the Oregon coast, some 2400 m beneath the surface, is not boiling. Provide an explanation.

How many calories are needed to change the temperature of 1 g of water by \(1^{\circ} \mathrm{C}\)? To melt 1 g of ice at \(0^{\circ} \mathrm{C}\)? To vaporize 1 g of boiling water at \(100^{\circ} \mathrm{C}\)?

Problem 30E Water will boil spontaneously in a vacuum—on the surface of the Moon, for example. Could you cook an egg in this boiling water? Explain.

Cite two reasons why firewalkers don’t burn their wetted feet when walking barefoot on red-hot coals.

Our inventor friend proposes a design for cookware that will allow boiling to occur at a temperature less than \(100^{\circ} \mathrm{C}\) so that food can be cooked with less energy consumption. Comment on this idea.

Problem 32E What can go wrong if you grasp the handle of a hot skillet with a wet thin dishcloth?

Problem 33E How can water be brought to a boil without heating it?

Problem 34E If water that boils due to reduced pressure is not hot, then is ice formed by the reduced pressure not cold? Explain.

Problem 35E Your instructor hands you a closed flask partly filled with room-temperature water. When you hold it, the heat transfer between your bare hands and the flask causes the water to boil. Quite impressive! How is this accomplished?

Problem 36E When you boil potatoes, will your cooking time be reduced with vigorously boiling water instead of gently boiling water? (Directions for cooking spaghetti call for vigorously boiling water—not to lessen cooking time but to prevent something else. If you don’t know what it is, ask a cook.)

Problem 37E Why does placing a lid over a pot of water on a stove shorten the time for the water to come to a boil, whereas, after the water is boiling, the use of a lid only slightly shortens the cooking time?

Problem 38E In the power plant of a nuclear submarine, the temperature of the water in the reactor is above 100°C. How is this possible?

Problem 39E Explain why the eruptions of many geysers repeat with notable regularity.

Why does the water in a car radiator sometimes boil explosively when the radiator cap is removed?

Problem 41E Can ice be colder than 0°C? What is the temperature of an ice-water, mixture?

Problem 42E Why is very cold ice “sticky”?

Problem 44E People who live where snowfall is common will tell you that air temperatures are higher when it’s snowing than when it's clear. Some misinterpret this by stating that snowfall can’t occur on very cold days. Explain this misinterpretation.

How does the freezing point of a liquid compare with its melting point?

Problem 45E How might water be desalinated by freezing?

Problem 46E Would regelation occur if ice crystals did not have an open structure? Explain.

Problem 47E A piece of metal and an equal mass of wood are both removed from a hot oven at equal temperatures and are dropped onto blocks of ice. The metal has a lower specific heat capacity than the wood. Which will melt more ice before cooling to 0°C?

How does melting ice change the temperature of the surrounding air?

Problem 49E When you step inside a warm ski lodge on a cold day, you find your eyeglasses fog. Why does this occur?

Problem 50E What accounts for the bulged ends of a can of soda that has been frozen?

Why is half-frozen fruit punch always sweeter than completely melted fruit punch?

Air-conditioning units contain no water whatever, yet it is common to see water dripping from them when they’re operating on a hot day. Explain.

Problem 53E Is it condensation or vaporization that occurs on the warm outside coils of an operating air conditioner?

Problem 54E Some old-timers found that when they wrapped newspaper around the ice in their iceboxes, melting was inhibited. Discuss the advisability of this practice.

Problem 55E When ice in a pond melts, what effect does this have on the temperature of the nearby air?

Why is it that a tub of water placed in a farmer’s canning cellar helps prevent canned food from freezing in cold winters?

Problem 57E Why will spraying fruit trees with water before a frost help to protect the fruit from freezing?

Problem 58E How can devices that heat homes in winter also be used to cool homes in summer?

Problem 59E Why does a hot dog pant?