Explanation Write the expression for work done in integral form. W = ∫ V 1 V 2 P d V (I) Here, W is the work done, V 1 is the initial volume, V 2 is the final volume, d V is the changing volume, and P is the pressure. The pressure is given by the van der wall’s equation. Write the van der wall’s equation. ( P + n 2 a V 2 ) ( V n − b ) = R T (II) Here, n is the number of moles, a , b are the van der wall’s constants, R is the universal gas constant, and T is the temperature. Solve equation (II) for P . ( P + n 2 a V 2 ) ( V n − b ) = R T ( P + n 2 a V 2 ) = R T ( V n − b ) P = R T ( V n − b ) − n 2 a V 2 = R T ( V n − b ) − a ( V n ) 2 (III) Use equation (III) in (I). W = ∫ V 1 V 2 ( R T ( V n − b ) − a ( V n ) 2 ) d V = ∫ V 1 V 2 ( n R T ( V − b n ) − a n 2 V 2 ) d V (IV) Integrate the equation (IV). W = [ n R T ln ( V − b n ) + a n 2 V ] V 1 V 2 = [ n R T ln ( V 2 − b n ) + a n 2 V 2 ] − [ n R T ln ( V 1 − b n ) + a n 2 V 1 ] = [ n R T ln ( V 2 − b n ) ( V 1 − b n ) + a n 2 ( 1 V 2 − 1 V 1 ) ] (V) Conclusion: Given that, number of moles is 1

Physics for Scientists and Engineers with Modern Physics

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ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 19, Problem 91GP

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Chapter 19 Solutions

Physics for Scientists and Engineers with Modern Physics

Ch. 19.2 - Return to the Chapter-Opening Question, page 496,...Ch. 19.5 - Prob. 1BE Ch. 19.5 - How much more ice at 10C would be needed in...Ch. 19.6 - What would be the internal energy change in...Ch. 19.7 - Is the work done by the gas in process ADB of Fig....Ch. 19.7 - In Example 1910, if the heat lost from the gas in...Ch. 19.10 - Fanning yourself on a hot day cools you by (a)...Ch. 19 - What happens to the work done on a jar of orange...Ch. 19 - Prob. 2Q Ch. 19 - Prob. 3Q

Ch. 19 - Prob. 4Q Ch. 19 - Prob. 5Q Ch. 19 - Why does water in a canteen stay cooler if the...Ch. 19 - Explain why burns caused by steam at 100C on the...Ch. 19 - Prob. 8Q Ch. 19 - Will potatoes cook faster if the water is boiling...Ch. 19 - Prob. 10Q Ch. 19 - Prob. 11Q Ch. 19 - Use the conservation of energy to explain why the...Ch. 19 - In an isothermal process, 3700 J of work is done...Ch. 19 - Explorers on failed Arctic expeditions have...Ch. 19 - Why is wet sand at the beach cooler to walk on...Ch. 19 - When hot-air furnaces are used to heat a house,...Ch. 19 - Is it possible for the temperature of a system to...Ch. 19 - Discuss how the first law of thermodynamics can...Ch. 19 - Explain in words why CP is greater than CV.Ch. 19 - Prob. 20Q Ch. 19 - An ideal monatomic gas is allowed to expand slowly...Ch. 19 - Ceiling fans are sometimes reversible, so that...Ch. 19 - Goose down sleeping bags and parkas are often...Ch. 19 - Microprocessor chips nowadays have a heat sink...Ch. 19 - Sea breezes are often encountered on sunny days at...Ch. 19 - The Earth cools off at night much more quickly...Ch. 19 - Explain why air-temperature readings are always...Ch. 19 - A premature baby in an incubator can be...Ch. 19 - Prob. 29Q Ch. 19 - A 22C day is warm, while a swimming pool at 22C...Ch. 19 - Prob. 32Q Ch. 19 - Prob. 33Q Ch. 19 - Prob. 34Q Ch. 19 - Prob. 35Q Ch. 19 - An emergency blanket is a thin shiny...Ch. 19 - Explain why cities situated by the ocean tend to...Ch. 19 - (I) To what temperature will 8700 J of heat raise...Ch. 19 - Prob. 2P Ch. 19 - Prob. 3P Ch. 19 - (II) A British thermal unit (Btu) is a unit of...Ch. 19 - Prob. 5P Ch. 19 - Prob. 6P Ch. 19 - (I) An automobile cooling system holds 18 L of...Ch. 19 - Prob. 8P Ch. 19 - (II) (a) How much energy is required to bring a...Ch. 19 - Prob. 10P Ch. 19 - Prob. 11P Ch. 19 - (II) A hot iron horseshoe (mass = 0.40kg), just...Ch. 19 - (II) A 31.5-g glass thermometer reads 23.6C before...Ch. 19 - Prob. 14P Ch. 19 - (II) When a 290-g piece of iron at 180C is placed...Ch. 19 - (II) The heat capacity. C, of an object is defined...Ch. 19 - (II) The 1.20-kg head of a hammer has a speed of...Ch. 19 - (I) How much heat is needed to melt 26.50kg of...Ch. 19 - (I) During exercise, a person may give off 180...Ch. 19 - (II) A 35g ice cube at its melting point is...Ch. 19 - (II) High-altitude mountain climbers do not eat...Ch. 19 - (II) An iron boiler of mass 180 kg contains 730kg...Ch. 19 - (II) In a hot days race, a bicyclist consumes 8.0...Ch. 19 - (II) The specific heat of mercury is 138 J/kg C....Ch. 19 - Prob. 25P Ch. 19 - (II) A 58-kg ice-skater moving at 7.5 m/s glides...Ch. 19 - (I) Sketch a PV diagram of the following process:...Ch. 19 - (I) A gas is enclosed in a cylinder fitted with a...Ch. 19 - (II) The pressure in an ideal gas is cut in half...Ch. 19 - (II) A 1.0-L volume of air initially at 3.5 atm of...Ch. 19 - (II) Consider the following two-step process. Heat...Ch. 19 - (II) The PV diagram in Fig. 1931 shows two...Ch. 19 - (II) Suppose 2.60 mol of an ideal gas of volume V1...Ch. 19 - (II) In an engine, an almost ideal gas is...Ch. 19 - (II) One and one-half moles of an ideal monatomic...Ch. 19 - (II) Determine (a) the work done and (b) the...Ch. 19 - (II) How much work is done by a pump to slowly...Ch. 19 - (II) When a gas is taken from a to c along the...Ch. 19 - (III) In the process of taking a gas from state a...Ch. 19 - (III) Suppose a gas is taken clockwise around the...Ch. 19 - (III) Determine the work done by 1.00 mol of a van...Ch. 19 - (I) What is the internal energy of 4.50 mol of an...Ch. 19 - Prob. 43P Ch. 19 - Prob. 44P Ch. 19 - Prob. 45P Ch. 19 - What gas is it? (II) Show that the work done by n...Ch. 19 - (II) An audience of 1800 fills a concert hall of...Ch. 19 - Prob. 48P Ch. 19 - Prob. 49P Ch. 19 - (III) A 1.00-mol sample of an ideal diatomic gas...Ch. 19 - (I) A 1.00-mol sample of an ideal diatomic gas,...Ch. 19 - (II) Show, using Eqs. 196 and 1915, that the work...Ch. 19 - (III) A 3.65-mol sample of an ideal diatomic gas...Ch. 19 - (II) An ideal monatomic gas, consisting of 2.8 mol...Ch. 19 - (III) A 1.00-mol sample of an ideal monatomic gas,...Ch. 19 - (III) Consider a parcel of air moving to a...Ch. 19 - Prob. 57P Ch. 19 - (I) One end of a 45-cm-long copper rod with a...Ch. 19 - (II) How long does it take the Sun to melt a block...Ch. 19 - (II) Heat conduction to skin. Suppose 150 W of...Ch. 19 - (II) A ceramic teapot ( = 0.70) and a shiny one (...Ch. 19 - (II) A copper rod and an aluminum rod of the same...Ch. 19 - Prob. 63P Ch. 19 - Prob. 64P Ch. 19 - (III) A house thermostat is normally set to 22C,...Ch. 19 - (III) Approximately how long should it take 9.5 kg...Ch. 19 - (III) A cylindrical pipe has inner radius R1 and...Ch. 19 - (III) Suppose the insulating qualities of the wall...Ch. 19 - Prob. 69GP Ch. 19 - (a) Find the total power radiated into space by...Ch. 19 - Prob. 71GP Ch. 19 - A mountain climber wears a goose-down jacket 3.5...Ch. 19 - Prob. 73GP Ch. 19 - Estimate the rate at which heat can he conducted...Ch. 19 - A marathon runner has an average metabolism rate...Ch. 19 - A house has well-insulated walls 19.5 cm thick...Ch. 19 - In a typical game of squash (Fig. 19-36), two...Ch. 19 - A bicycle pump is a cylinder 22 cm long and 3.0 cm...Ch. 19 - Prob. 79GP Ch. 19 - The temperature within the Earths crust increases...Ch. 19 - An ice sheet forms on a lake. The air above the...Ch. 19 - An iron meteorite melts when it enters the Earths...Ch. 19 - A scuba diver releases a 3.60-cm-diameter...Ch. 19 - A reciprocating compressor is a device that...Ch. 19 - The temperature of the glass surface of a 75-W...Ch. 19 - Suppose 3.0 mol of neon (an ideal monatomic gas)...Ch. 19 - At very low temperatures, the molar specific heat...Ch. 19 - A diesel engine accomplishes ignition without a...Ch. 19 - When 6.30 105 J of heat is added to a gas...Ch. 19 - In a cold environment, a person can lose heat by...Ch. 19 - Prob. 91GP

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The total work done.

Solution Summary: The author writes the expression for work done in integral form. The pressure is given by the van der wall’s equation.

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Chapter 19 Solutions