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physics
thermodynamics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

A monatomic gas and a diatomic gas both have n moles and are at temperature T. What is the difference in their internal energies? Express your answer in n, R, and T.
What types of energy make up the internal energy of monatomic gases? How about diatomic gases?
A person running a fever has a body temperature of 40 oC. What is this temperature on the Fahrenheit scale?
The temperature drops from 60° F during the day to 35°F during the night. (a) The corresponding temperature drop on the Celsius scale is (1) greater than, (2) the same as, or (3) less than. Explain. (b) Compute the temperature drop on the Celsius scale.
There is one temperature at which the Celsius and Fahrenheit scales have the same reading. (a) To find that temperature, would you set (1) STF = 9TC (2) 9T+ = 5TC or (3) TF = TC Why? (b) Find the temperature.
(a) The largest temperature drop recorded in the United States in one day occurred in Browning, Montana, in 1916, when the temperature went from 7oC to – 49oC. What is the corresponding change on the Fahrenheit scale? (b) On the Moon, the average surface temperature is 127oC during the day and
Astronomers know that the temperatures of stellar interiors are €œextremely high.€ By this they mean they can convert from Fahrenheit to Celsius temperature using a rough rule of thumb:(a) Determine the exact fraction (it isn€™t 1/2) and (b) The percentage error
Fig. 10.5 is a plot of Fahrenheit temperature versus Celsius temperature.(a) Is the value of the y-intercept found by setting (1) TF = TC, (2) TC = 0, or (3) TF = 0? Why? (b) Compute the value of the y-intercept. (c) What would be the slope and y-intercept if the graph were plotted the opposite
Convert the following temperatures to absolute temperatures in kelvins: (a) 0oC, (b) 100oC, (c) 20 oC, and (d) - 35oC.
Convert the following temperatures to Celsius: (a) 0 K, (b) 250 K, (c) 273 K, and (d) 325 K.
(a) Derive an equation for converting Fahrenheit temperatures directly to absolute temperatures in kelvins. (b) Which is the lower temperature, or 300 K?
When lightning strikes, it can heat the air around it to more than 30 000 K, five times the surface temperature of the Sun. (a) What is this temperature on the Fahrenheit and Celsius scales? (b) The temperature is some-times reported to be 30 000 oC. Assuming that 30 000 K is correct, what is the
How many moles are in (a) 40 g of water, (b) 245 g of CO2 (carbon dioxide), (c) 138 g of N2 (nitrogen), and (d) 56 g of O2 (oxygen) at STP?
Convert the following to Celsius readings: (a) 80 oF, (b) 0 oF, and (c) - 10 oF.
(a) In a constant volume gas thermometer, if the pressure of the gas decreases, has the temperature of the gas (1) increased, (2) decreased, or (3) remained the same? Why? (b) The initial absolute pressure of a gas is 1000 Pa at room temperature (20 oC). If the pressure increases to 1500 Pa, what
If the pressure of an ideal gas is doubled while its absolute temperature is halved, what is the ratio of the final volume to the initial volume?
Show that 1.00 mol of ideal gas under STP occupies a volume of 0.0224 m3.
What volume is occupied by 160 g of oxygen under a pressure of 2.00 atm and a temperature of 300 K?
An athlete has a large lung capacity, 7.0 L. Assuming air to be an ideal gas, how many molecules of air are in the athlete’s lungs when the air temperature in the lungs is 37 oC under normal atmospheric pressure?
Is there a temperature that has the same numerical value on the Kelvin and the Fahrenheit scales? Justify your answer.
A husband buys a helium-filled anniversary balloon for his wife. The balloon has a volume of 3.5 L in the warm store at 74 oF. When he takes it outside, where the temperature is 48 oF, he finds it has shrunk. By how much has the volume decreased?
An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of 30 oC. Later it is driven to a place where the temperature is only – 20 oC. What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is
On a warm day (92 oF), an air-filled balloon occupies a volume of and has a pressure of 20.0 lb/in2. If the balloon is cooled to 32 oF in a refrigerator while its pressure is reduced to 14.7 lb/in2, what is the volume of the air in the container? (Assume that the air behaves as an ideal gas.)
A steel-belted radial automobile tire is inflated to a gauge pressure of when the temperature is 61 oF. Later in the day, the temperature rises to 100 oF. Assuming the volume of the tire remains constant, what is the tire’s pressure at the elevated temperature?
Convert the following to Fahrenheit readings: (a) 120 oC (b) 12 oC and (c) - 5 oC
A scuba diver takes a tank of air on a deep dive. The tank’s volume is 10 L and it is completely filled with air at an absolute pressure of 232atm at the start of the dive. The air temperature at the surface is and the diver ends up in deep water at 60 oF. Assuming thermal equilibrium and
(a) If the temperature of an ideal gas increases and its volume decreases, will the pressure of the gas (1) increase, (2) remain the same, or (3) decrease? Why? (b) The Kelvin temperature of an ideal gas is doubled and its volume is halved. How is the pressure affected?
If 2.4 m3 of a gas initially at STP is compressed to 1.6 m3 and its temperature is raised to 30 oC, what is its final pressure?
The pressure on a low-density gas in a cylinder is kept constant as its temperature is increased. (a) Does the volume of the gas (1) increase, (2) decrease, or (3) remain the same? Why? (b) If the temperature is increased from 10 oC to 40 oC, what is the percentage change in the volume of the gas?
A diver releases an air bubble of volume 2.0 cm3 from a depth of 15 m below the surface of a lake, where the temperature is 7.0° C. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is 20 ° C?
(a) Show that for the Kelvin temperature range(b) For room temperature, what percentage error would result from using this estimation to determine the Kelvin temperature? (c) For a typical stellar interior temperature of 10 million oF, what is the percentage error in the Kelvin temperature? (Carry
A steel beam 10 m long is installed in a structure at 20 oC. What is the beam’s change in length when the temperature reaches (a) – 25 oC and (b) 45 oC?
An aluminum tape measure is accurate at 20 oC. (a) If the tape measure is placed in a freezer, would it read (1) high, (2) low, or (3) the same? Why? (b) If the temperature of the freezer is – 5.0 oC, what would be the stick’s percentage error because of thermal contraction?
Concrete highway slabs are poured in lengths of 5.00 m. How wide should the expansion gaps between the slabs be at a temperature of 20 oC to ensure that there will be no contact between adjacent slabs over a temperature range of to – 25 oC to 45 oC?
A man’s gold wedding ring has an inner diameter of 2.4 cm at 20 oC. If the ring is dropped into boiling water, what will be the change in the inner diameter of the ring?
Which is the lower temperature: (a) 245 oC or 245 oF? (b) 200 oC or 375 oF?
A circular steel plate of radius 15 cm is cooled from 350 oC to 20 oC. By what percentage does the plate’s area decrease?
What temperature change would cause a 0.20% increase in the volume of a quantity of water that was initially at 20 oC?
Apiece of copper tubing used in plumbing has a length of 60.0 cm and an inner diameter of 1.50 cm at 20 oC. When hot water at flows through the tube, what are (a) The tube’s new length and (b) The change in its cross-sectional area? Does the latter affect the flow speed?
A pie plate is filled up to the brim with pumpkin pie filling. The pie plate is made of Pyrex and its expansion can be neglected. It is a cylinder with an inside depth of 2.10 cm and an inside diameter of 30.0 cm. It is prepared at a room temperature of 68 oF and placed in an oven at 400 oF. When
A circular piece is cut from an aluminum sheet at room temperature. (a) When the sheet is then placed in an oven, will the hole (1) get larger, (2) get smaller, or (3) remain the same? Why? (b) If the diameter of the hole is 8.00 cm at 20° C and the temperature of the oven is , what will be the
In Fig. 10.20, the steel ring of diameter 2.5 cm is 0.10 mm smaller in diameter than the steel ball at 20° C.(a) For the ball to go through the ring, should you heat (1) the ring, (2) the ball, or (3) both? Why? (b) What is the minimum required temperature?
When exposed to sunlight, a hole in a sheet of copper expands in diameter by 0.153% compared to its diameter at 68 °C. What is the Celsius temperature of the copper sheet in the sun?
One morning, an employee at a rental car company fills a car’s steel gas tank to the top and then parks the car a short distance away. (a) That afternoon, when the temperature increases, will any gas overflow? Why? (b) If the temperatures in the morning and afternoon are, respectively, 10 °C
A copper block has an internal spherical cavity with a 10-cm diameter (Fig. 10.23). The block is heated in an oven 20° C from to 500 K.(a) Does the cavity get larger or smaller? (b) What is the change in the cavity€™s volume?
A brass rod has a circular cross-section of radius 5.00 cm. The rod fits into a circular hole in a copper sheet with a clearance of 0.010 mm completely around it when both the rod and the sheet are at 20 °C. (a) At what temperature will the clearance be zero? (b) Would such a tight fit be
The coldest inhabited village in the world is Oymyakon, a town located in eastern Siberia, where it gets as cold as – 94 oF. What is this temperature on the Celsius scale?
An aluminum rod is measured with a steel tape at 20 °C, and the length of the rod is found to be 75 cm. What length will the tape indicate when both the rod and the tape are at (a) – 10 °C ? (b) 50 °C?
Table 10.1 states that the (experimental) coefficient of volume expansion for air (and most other ideal gases at 1 atm and 20 °C) is 3.5 x 10-3/oC. Use the definition of the volume expansion coefficient to show that this value can, to a very good approximation, be predicted from the ideal gas law
A Pyrex beaker that has a capacity of 1000 cm3 at 20 °C contains 990 cm3 of mercury at that temperature. Is there some temperature at which the mercury will completely fill the beaker? Justify your answer. (Assume that no mass is lost by vaporization and include the expansion of the beaker.)
If the average kinetic energy per molecule of a monatomic gas is 7.0 x 10-21 J, what is the Celsius temperature of the gas?
What is the average kinetic energy per molecule in a monatomic gas at (a) 10 °C and (b) 90 °C?
If the Celsius temperature of a monatomic gas is doubled, (a) will the internal energy of the gas (1) double, (2) increase by less than a factor of 2, (3) be half as much, or (4) decrease by less than a factor of 2? Why? (b) If the temperature is raised from 20 °C to 40 °C, what is the ratio of
What is the rms speed of the molecules in low-density oxygen gas at 0 °C? (The mass of an oxygen molecule, O2, is 5.31 x 10-26 kg).
(a) What is the average kinetic energy per molecule of a monatomic gas at a temperature of 25 °C? (b) What is the rms speed of the molecules if the gas is helium? (A helium molecule consists of a single atom of mass 6.65 x 10-27 kg).
(a) Estimate the total amount of translational kinetic energy in a small classroom at normal room temperature. Assume the room measures 4.00 m by 10.0 m by 3.00 m. (b) If this energy were all harnessed, how high would it be able to lift an elephant with a mass of 1200 kg?
A quantity of an ideal gas is at 0 °C. An equal quantity of another ideal gas is at twice the absolute temperature. What is its Celsius temperature?
The highest and lowest recorded air temperatures in the world are, respectively, 58 oC (Libya, 1922) and – 89 oC (Antarctica, 1983). What are these temperatures on the Fahrenheit scale?
A sample of oxygen (O2) and another sample of nitrogen (N2) are at the same temperature. (a) The rms speed of the nitrogen sample is (1) greater than, (2) the same as, or (3) less than the rms speed of the oxygen sample. Explain. (b) Calculate the ratio of the rms speed in the nitrogen sample to
If 2.0 mol of oxygen gas is confined in a 10-L bottle under a pressure of 6.0 atm, what is the average kinetic energy of an oxygen molecule?
If the temperature of an ideal gas increases from 300 K to 600 K, what happens to the rms speed of the gas molecules?
If the temperature of an ideal gas is raised from 25 °C to 100 °C, how much faster is the new rms speed of the gas molecules?
If the rms speed of the molecules in an ideal gas at 20 °C increases by a factor of 2, what is the new Celsius temperature?
During the race to develop the atomic bomb in World War II, it was necessary to separate a lighter isotope of uranium (U-235 was the fissionable one needed for bomb material) from a heavier variety (U-238). The uranium was converted into a gas, uranium hexafluoride (UF6), and the two uranium
What is the total internal energy of 1.00 mol of 30°C. He gas and O2 gas, respectively?
If 1.0 mol of a monatomic gas has a total internal energy of at a certain temperature, what is the total internal energy of 1.0 mol of a diatomic gas at the same temperature?
For an average molecule of N2 gas at 10 °C, what are its (a) Translational kinetic energy, (b) Rotational kinetic energy, and (c) Total energy? Repeat for He gas at the same temperature.
A diatomic gas has a certain total kinetic energy at 25 °C. If a monatomic gas of the same number of molecules as the diatomic gas has the same total kinetic energy, what is the Celsius temperature of the monatomic gas?
The highest and lowest recorded air temperatures in the United States are, respectively, 134 oF (Death Valley, California, 1913) and – 80 oF (Prospect Creek, Alaska, 1971). What are these temperatures on the Celsius scale?
(a) When cooled, the densities of most objects (1) increase, (2) decrease, (3) stay the same. (b) By what percentage does the density of a bowling ball change (assuming it is a uniform sphere) when it is taken from room temperature (68oF) into the cold night air in Nome, Alaska (–40oF). Assume
When a full copper kettle is tipped vertically at room temperature (68oF), water initially pours out of its spout at 100 cm3 / s (cubic centimeters per second). By what percentage will this change if the kettle instead contains boiling water at 212 oF? Assume that the only significant change is due
An ideal gas sample occupies a container of volume 0.75 L at STP. Find (a) The number of moles and (b) The number of molecules in in the sample. (c) If the gas is car-bon monoxide (CO), what is the sample’s mass?
2.00 mol of a monatomic gas at atmospheric pressure has a total internal energy of 7.48 x 103J. What is the volume occupied a rigid cylinder by the gas?
An ideal gas in a cylinder is at 20 oC and 2.0 atm. If it is heated so its rms speed increases by 20%, what is its new pressure?
The escape speed from the Earth is about 11 000 m/s (Section 7.5). Assume that for a given type of gas to eventually escape the Earth’s atmosphere, its average molecular speed must be about of the escape speed. (a) Which gas would be more likely to escape the Earth: (1) oxygen, (2) nitrogen, or
During open-heart surgery it is common to cool the patient’s body down to slow body processes and gain an extra margin of safety. A drop of 8.5 oC is typical in these types of operations. If a patient’s normal body temperature is 98.2 oF, what is her final temperature in both Celsius and
In the troposphere (the lowest part of the atmosphere), the temperature decreases rather uniformly with altitude at a so-called “lapse” rate of about 6.5 oC. What are the temperatures (a) Near the top of the troposphere (which has an average thickness of 11 km) and (b) Outside a commercial
In general, you would get a more severe burn from steam at 100oC than from the same mass of hot water at 100oC. Why?
Why is the warning shown on the highway road sign in Fig. 11.20 necessary?
Explain how the Thermos bottle shown in Fig. 11.17 can minimize all mechanisms of heat transfer.
What is the main difference between internal energy and heat?
If someone says that a hot object contains more heat than a cold one, would you agree? Why?
At a lake, does the lake water or the lake beach get hotter during a summer day? Which gets colder during a winter night? Explain.
Many people have performed firewalking, in which a bed of red- hot coals (temperature over) is walked on with bare feet. (You should not try this at home!) How is this possible?
A hot steel ball is dropped into a cold aluminum cup containing some water. ( Assume the system is an isolated.) If the ball loses 400 J of heat, what can be said according to calorimetry?
Discuss the energy conversion in the process of adding heat to an object that is undergoing a phase change.
A window air conditioner has a rating of 20 000 Btu/h. What is this rating in watts?
Equal amounts of heat are added to an aluminum block and a copper block of different masses to achieve the same temperature increase. (a) The mass of the aluminum block is (1) more, (2) the same, (3) less than the mass of the copper block. Why? (b) If the mass of the copper block is 3.00 kg, what
A modern engine of alloy construction consists of 25 kg of aluminum and 80 kg of iron. How much heat does the engine absorb as its temperature increases from 20 oC to 100 oC as it warms up to operating temperature?
Equal amounts of heat are added to different quantities of copper and lead. The temperature of the copper increases by 5.0oC and the temperature of the lead by 10 oC. (a) The lead has (1) a greater mass than the copper, (2) the same amount of mass as the copper, (3) less mass than the copper. (b)
Initially at 20 oC, 0.50 kg of aluminum and 0.50 kg of iron are heated to 100 oC. (a) The aluminum gains (1) more heat than the iron, (2) the same amount of heat as the iron, (3) less heat than the iron. Why? (b) Calculate the difference in heat required to prove your answer to part (a).
A 0.20-kg glass cup at is filled with 0.40 kg of hot water at 90 oC. Neglecting any heat losses to the environment, what is the equilibrium temperature of the water?
A 0.250-kg coffee cup at 20 oC is filled with 0.250 kg of brewed coffee at 100 oC. The cup and the coffee come to thermal equilibrium at 80 oC. If no heat is lost to the environment, what is the specific heat of the cup material?
An aluminum spoon at 100 oC is placed in a Styrofoam cup containing 0.200 kg of water at 20 oC. If the final equilibrium temperature is and no heat is lost to the cup itself or the environment, what is the mass of the aluminum spoon?
A student doing an experiment pours 0.150 kg of heated copper shot into a 0.375-kg aluminum calorimeter cup containing 0.200 kg of water. The cup and water are both initially at 25 oC. The mixture (and the cup) comes to thermal equilibrium at 28 oC. What was the initial temperature of the shot?
At what average rate would heat have to be removed from 1.5 L of (a) Water and (b) Mercury to reduce the liquid’s temperature from 20oC to its freezing point in 3.0 min?
When resting, a person gives off heat at a rate of about 100 W. If the person is submerged in a tub containing 150 kg of water at 27oC and the heat from the person goes only into the water, how many hours will it take for the water temperature to rise to 28oC?
A person goes on a 1500-Cal-per-day diet to lose weight. What is his daily energy allowance expressed in joules?
To determine the specific heat of a new metal alloy, 0.150 kg of the substance is heated to 400oC and then placed in a 0.200-kg aluminum calorimeter cup containing 0.400 kg of water at 10.0oC. If the final temperature of the mixture is 30.5oC, what is the specific heat of the alloy? (Ignore the
In a calorimetry experiment, 0.50 kg of a metal at 100oC is added to 0.50 kg of water at in an aluminum calorimeter cup. The cup has a mass of 0.250 kg. (a) If some water splashed out of the cup when the metal was added, the measured specific heat will appear to be (1) higher, (2) the same, (3)

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