PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HOMEWORK PROBLEMS Chapter 10 THERMAL PHYSICS HW 10 PART A Hand in your answers in class on scantron on Monday November 2010 Write your name class 1401 and HW 10 on the scantron 1 On a very cold day in upstate New York the temperature is 25 C which is equivalent to what temperature in Fahrenheit a 46 F b 77 F c 18 F d 298 K e 13 F TF 95 TC 32 95 25 32 13 F 2 Convert 162 F to the equivalent temperature in Kelvin a 373 K b 288 K c 345 K d 201 K e 308 K TC 95 TF 32 95 162 32 72 2 C then TK TC 273 72 2 273 345 K 3 The Statue of Liberty is 93 m tall on a summer morning when the temperature is 20 C If the temperature of the statue rises from 20 C to 30 C what is the order of magnitude of the statue s increase in height Choose the best estimate treating the statue as though it were solid copper a 0 1 mm b 1 mm c 1 cm d 10 cm e 1 m 1 DL a Cu L0 DT 17 10 6 C C 1 6 10 2 m 1 6 cm 93 m 10 4 A hole is drilled in a metal plate When the metal is heated what happens to the diameter of the hole a It decreases b It increases c It remains the same d The answer depends on the initial temperature of the metal e None of these The correct choice is b When a solid containing a cavity is heated the cavity expands in the same way as it would if filled with the material making up the rest of the object 5 A container holds 0 50 m3 of oxygen at an absolute pressure of 4 0 atm A valve is opened allowing the gas to drive a piston increasing the volume of the gas until the pressure drops to 1 0 atm If the temperature remains constant what new volume does the gas occupy a 1 0 m3 b 1 5 m3 c 2 0 m3 d 0 12 m3 e 2 5 m3 From the ideal gas law with the mass of the gas constant P2V2 T2 P1V2 T1 Thus P T V2 1 2 V1 4 1 0 50 m 3 2 0 m 3 P2 T1 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 10 6 If the volume of an ideal gas is doubled while its temperature is quadrupled does the pressure a remain the same b decrease by a factor of 2 c decrease by a factor of 4 d increase by a factor of 2 or e increase by a factor of 4 From the ideal gas law with the mass of the gas constant P2V2 T2 P1V2 T1 Thus V T 1 P2 1 2 P1 4 P1 2 P1 2 V2 T1 7 One way to cool a gas is to let it expand When a certain gas under a pressure of 5 00 106 Pa at 25 0 C is allowed to expand to 3 00 times its original volume its final pressure is 1 07 X 106 Pa What is its final temperature a 177 C b 233 K c 212 K d 191 K e 115 K Remember that one must use absolute temperatures and pressures in the ideal gas law Thus the original temperature is TK TC 273 15 25 273 15 298 K and with the mass of the gas constant the ideal gas law gives P V 1 07 106 Pa T2 2 2 T1 3 00 298 K 191 K 5 00 106 Pa P1 V1 8 What is the internal energy of 26 0 g of neon gas at a temperature of 152 C a 2 440 J b 6 830 J c 3 140 J d 5 870 J e 5 020 J 3 The internal energy of n moles of a monatomic ideal gas is U 2 nRT where R is the universal gas constant and T is the absolute temperature of the gas For the given neon sample T TC 273 15 152 273 15 K 425 K and n 26 0 g 1 29 mol 20 18 g mol 3 3 Thus U 2 1 29 mol 8 31 J mol K 425 K 6 83 10 J 9 Find the root mean square speed of a methane gas molecule CH4 at 25 0 C a 545 m s b 681 m s c 724 m s d 428 m s e 343 m s The root mean square speed of molecules in a gas with molar mass M expressed in kilograms per mole and absolute temperature T is vrms 3RT M The molar mass of methane CH4 is g 1 kg M 12 0 4 1 00 1 6 10 2 kg mol mol 103 g and its absolute temperature is T TC 273 15 25 0 273 15 K 298 K Therefore vrms 3 8 31 J mol K 298 K 1 60 10 2 kg mol 681 m s 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 10 10 Which of the assumptions below is not made in the kinetic theory of gases a The number of molecules is very small b The molecules obey Newton s laws of motion c The collisions between molecules are elastic d The gas is a pure substance e The average separation between molecules is large compared with their dimensions The kinetic theory of gases does assume that the molecules in a pure substance obey Newton s laws and undergo elastic collisions and the average distance between molecules is very large in comparison to molecular sizes However it also assumes that the number of molecules in the sample is large so that statistical averages are meaningful The untrue statement included in the list of choices is a 11 Suppose for a brief moment the gas molecules hitting a wall stuck to the wall instead of bouncing off the wall How would the pressure on the wall be affected during that brief time a The pressure would be zero b The pressure would be halved c The pressure would remain unchanged d The pressure would double e The answer would depend on the area of the wall In a head on elastic collision with a wall the change in momentum of a gas molecule is Dp m v f v0 m v0 v0 2 mv0 If the molecule should stick to the wall instead of rebounding the change in the molecule s momentum would be Dp m 0 v0 mv0 which is half that in the elastic collision Since a gas exerts a pressure on its container by molecules imparting impulses to the walls during collisions and the impulse imparted equals the magnitude of the change in the molecular momentum decreasing the change in momentum during the collisions by a factor of 2 would …