Ch18Word - Chapter 18 CHAPTER 18 Kinetic Theory of Gases 1....

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Chapter  18 CHAPTER 18 – Kinetic Theory of Gases 1. ( a ) The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT  =  * (1.38 × 10 –23   J/K)(273 K) =         5.65 × 10 –21  J . ( b ) For the total translational kinetic energy we have K N ( ! mv rms 2 ) =  * nN A kT   * (2.0 mol)(6.02 × 10 23  molecules/mol)(1.38 × 10 –23   J/K)(293 K) =         7.3 × 10 3  J . 2. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT , which gives v rms  = (3 kT / m ) 1/2   = [3(1.38 × 10 –23   J/K)(6000 K)/(4 u)(1.66 × 10 –27  kg/u)] 1/2  =        6.1 × 10 3  m/s . 3. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT . If we form the ratio for the two temperatures, we have ( v rms2 / v rms1 ) 2  =  T 2 / T 1  = 373 K/273 K, which gives  v rms2 / v rms1  =        1.17 . 4. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT We form the ratio at the two temperatures: ( v rms2 / v rms1 ) 2  =  T 2 / T 1   ; (2) 2  =  T 2 /293 K, which gives  T 2  = 1172 K =        899°C . 5. ( a ) We find the mean  speed  from v rms  = (? v )/ N  = (6 + 2 + 4 + 6 + 0 + 4 + 1 + 8 + 5 + 3 + 7 + 8)/12 =        4.5 . ( b ) We find the rms speed  from v rms  = [(? v 2 )/ N ] 1/2  = [(6 2  + 2 2  + 4 2  + 6 2  + 0 2  + 4 2  + 1 2  + 8 2  + 5 2  + 3 2  + 7 2  + 8 2 )/12] 1/2  =        5.2 . Note that this is greater than the mean  speed  of 4.5. 6. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT We treat the small changes as differentials.  We find the relationship  between  the changes by  differentiating: mv rms  d v rms  =  * k  d T ,  or, after dividing  by  ! mv rms 2  =  * kT , 2 d v rms / v rms  = d T / T ; 2(0.010 v rms )/ v rms  = d T /293.2 K, which gives d T  = 5.9 K. Thus the new  temperature  is  T  + d T  = 293.2 K + 5.9 K = 299.1 K =        25.9°C . 7. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT We form the ratio at the two temperatures, and  use the ideal gas law: ( v rms2 / v rms1 ) 2  =  T 2 / T 1  =  P 2 V 2 / P 1 V 1  =  P 2 / P 1  ; ( v rms2 / v rms1 ) 2  = 2, which gives  v rms2 / v rms1  =        v2 . 8. The average kinetic energy depends  on the temperature: ! mv rms 2  =  * kT ,   or    kT / m  =  @ v rms 2 . With 
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Ch18Word - Chapter 18 CHAPTER 18 Kinetic Theory of Gases 1....

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