phys 369 09 hw 7 Solutions

phys 369 09 hw 7 Solutions - Phys. 369, Fall 2009 Homework...

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1 Phys. 369, Fall 2009 Homework #7 Solutions 1. (12 points)
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2 2. (12 points) 3. (14 points) a) The volume of the gas is () 33 3 1000 cm 1 m 1 liter 1.0 10 m . liter 100 cm V × = × Its pressure is 55 Pa 3 atm 1.013 10 3.09 10 Pa. atm P × = × The number of atoms is 53 22 23 3.09 10 10 3.73 10 . 1.381 10 600 PV N kT ×× == Helium is a monatomic nearly ideal gas, so the internal energy of the gas is 22 23 3 1.5 3.73 10 1.381 10 600 463 J 2 UN k T × × × × × = The mass of a helium atom is 27 27 4 u 4 1.661 10 kg 6.64 10 kg. m −− × × = ×
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3 The argument of the logarithm in the Sackur-Tetrode equation is () 3/2 32 7 5 2 22 2 22 34 4 10 4 6.64 10 463 5.91 10 33 . 7 3 1 0 3 3.73 10 6.626 10 Vm U NN h ππ −− ⎛⎞ ×× × ⎜⎟ == × × ⎝⎠ ××× × The entropy of the gas is given by the Sackur-Tetrode equation as 22 23 5 2 45 J ln 3.73 10 1.381 10 ln 5.91 10 2.5 8.13 K U SN k h π =+ = × × × × + = The enthalpy of the gas is ( ) 53 463 3.09 10 10 463 309 772 J HUP V = +=+ × × =+= . Its Helmholtz free energy is ( ) 463 600 8.13 4415 J FUT S =− = − × = .
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This note was uploaded on 11/06/2010 for the course PHY 369 taught by Professor Staff during the Fall '08 term at University of Texas at Austin.

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phys 369 09 hw 7 Solutions - Phys. 369, Fall 2009 Homework...

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