ps10_soln

# ps10_soln - Physics 105 Problem Set 10 Solutions Problem...

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Physics 105 Problem Set 10 Solutions Problem 1 (4 pts) 1. (Fermi 10.1) Calculate the work done in isobaric expansion. W = Z V f V i pdV p = 2 . 34 atm = 2 . 37 × 10 5 N/m 2 , V i = 3 . 12 litres = 3 . 12 × 10 - 3 m 3 , V f = 4 . 01 litres = 4 . 01 × 10 - 3 m 3 ; W = P ( V f - V i ) = 211 J 2. (Fermi 10.2) Use the ideal gas law: pV = nRT . The number of moles is n = 30 2 = 15, at the temperature T = 291 K . Volume is V = 1 m 3 . This gives for the pressure p = 3 . 6 × 10 4 N/m 2 = 0 . 36 atm . 3. (Fermi 10.4) Calculate the work done in isothermal expansion: dW = pdV , V = nRT/p . Thus dV = nRTd 1 p = - nRT p 2 dp (T is constant) and 1 W = - nRT Z P f P i dp p = nRT log( p i /p f ) . 32 grams of oxygen (remember that oxygen O 2 is a di-atomic molecule) make up a mole, so 10 grams make up 0.312 mole; i.e., n = 0 . 312. Temperature is T = 20 C = 293 K , pressure p i = 1 atm = 1 . 01 × 10 5 N/m 2 , p f = 0 . 3 atm = 3 . 03 × 10 4 N/m 2 . W = 915 J . 4. Volume of one mole of an ideal gas at STP V can be found from the equation of state of an ideal gas: P atm V = RT . The size of the cube containing one molecule in average is L gas = 3 r V N A = 3 r RT P atm N A = 3 . 4 · 10 - 9 m = 3 . 4nm .

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