P2213_HW01_solns_Fall2008 - Physics 2213 HW #1 Solutions...

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- 1 - Physics 2213 HW #1 — Solutions Fall 2008 18.6 [Balloons] We have pV nRT = for an ideal gas and tot m nM = for the mass of the gas. The temperature must be converted to Kelvin: 22.0 C 295.15K. T = ° = The average molar mass of air is 3 28.8 10 kg mol M - = × . For helium 3 4.00 10 kg mol M - = × . Next, we need to check units for pressure and volume, and make sure they are consistent with those of the gas constant R . Since we are using SI units in this course, we need to convert the pressure value from atm to Pa, and the volume from L to m 3 : 5 1 atm 1.01 10 Pa p = = × , and 4 3 0.9 L 9 10 m V - = = × . (a) 5 4 3 3 3 tot (1.01 10 Pa)(9 10 m )(28.8 10 kg/mol) 1.07 10 kg . (8.31 J/mol K)(295.15 K) pV m nM M RT - - - × × × = = = = × (b) 5 4 3 3 4 tot (1.01 10 Pa)(9 10 m )(4 10 kg/mol) 1.48 10 kg . (8.31 J/mol K)(295.15 K) pV m nM M RT - - - × × × = = = = × 18.7 [Jaguar XK8] We are asked to compare two states. Use the ideal gas law to obtain 2 T in terms of 1 T and ratios of
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P2213_HW01_solns_Fall2008 - Physics 2213 HW #1 Solutions...

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