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# hw1 - (you can take the depth=1 for convenience Show how...

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MAE135 Homework No. 1 Spring 2010 Date assigned: March 24, 2010 Due date: 5:00 pm, Tuesday, April 6, 2010 Assume calorically-perfect gas with γ =1.4 for all problems. PROBLEM 1 (5 points) The internal energy per unit mass is e = c v T while the kinetic energy per unit mass is 1 2 V 2 . For air at room temperature (290 K), calculate the ratio of kinetic over internal energy. Plot the result (Excel or similar) for V =0 to 1000 m/s. PROBLEM 2 (10 points) R dR p The expression for moving boundary work δW = - pd V is usually derived using the one-dimensional piston example, as shown in class and found in numer- ous thermodynamics textbooks. It is then claimed that the relation is valid for any shape boundary. Well, let us test this claim for a cylindrical-shaped boundary with initial radius R , later compressed to a radius R - dR , where dR << R . You will be dealing with work per unit depth
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Unformatted text preview: (you can take the depth=1 for convenience). Show how you de±ne the work for this boundary and prove that the above relation still holds. PROBLEM 2 (15 points) p 1 T 1 1 p 2 = 2 p 1 T 2 2 Isothermal or Isentropic A gas particle is initially at pressure p 1 and has a volume V 1 and temperature T 1 . We follow this particle (we track the same mass) as it undergoes a process whereby the ±nal pressure is p 2 = 2 p 1 . Consider two processes: Isothermal and Isentropic. For each process, ±nd: (a) the ±nal volume ratio V 2 / V 1 ; (b) the ±nal temperature ratio T 2 /T 1 ; (c) the work per unit mass w =-i 2 1 pdv done on the particle. Express your answer in the form w/ ( p 1 v 1 ) = ... ; (d) the entropy change (per unit mass) normalized by the gas constant, ( s 2-s 1 ) /R . 1...
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