PS5F07 - Chemistry 391 Problem Set 5 (Due, Monday October...

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Chemistry 391 Fall 2007 Problem Set 5 (Due, Monday October 8) 1. The Gibbs differentials imply that pV GA S TT ∂∂ =− ⎟⎟ . This is a remarkable result. Prove it from the defining relation () ( ) ,, , ) , GTp ATVTp pVTp =+ . 2. You have containers of pure H 2 and He at 298 K and 1 atm pressure. Calculate mixing mixing GT S Δ= Δ relative to the unmixed gases of a. a mixture of 10 mol of H 2 and 10 mol of He b. a mixture of 10 mol of H 2 and 20 mol of He c. For what composition (proportion of the two gases) does mixing G Δ have its minimum value? Explain physically and show it with calculus. 3. Show that P p V dH C dT V T dp T ⎡⎤ ⎛⎞ ⎢⎥ ⎜⎟ ⎝⎠ ⎣⎦ . (These are all easily measurable properties for a gas and are useful for e.g. Joule-Thompson calculations). HINT – It will prove useful to consider GHT S and what this produces for T G p
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