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HW4-2009

# HW4-2009 - under the assumption of an ideal gas(b Calculate...

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ECH 152A, Fall 2009, Roland Faller Homework 4, October 16, 2009 Due: October 23, Beginning of Lecture 1. (4 points) A house has to be modeled as an open system as air can leave and enter and heating at constant pressure leads to leaking of air to the outside. Show that . Q = - PV dn dt + n dU dt . The quantities refer to the house. 2. (4 points) (a) Express the volume expansivity and the isothermal compressibility as func- tions of density and its derivatives. (b) The compressibility of water at 50 C is κ T = 44 . 18 × 10 - 6 bar - 1 and we assume it does not depend on pressure. We start with 1 bar, at what pressure is the volume 99% of the starting volume. 3. (6 points) (This problem is based on an old Midterm 2 problem) We isothermally compress one mole of nitrogen at 0 C from 100 kpa to 10 MPa. (a) Calculate the work, the heat and the change in internal energy and volume
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Unformatted text preview: under the assumption of an ideal gas. (b) Calculate the work required if we assume the virial equation below. Use the initial and ﬁnal volumes from part (a). If you cannot solve part (a) calculate the work for decreasing volume by a factor of 10 for partial credit. Do not iterate. pV RT = 1 + B V + C V 2 with B =-10 . 3 × 10-6 m 3 mole and C = 1 . 517 × 10-9 m 6 mole 2 . 4. (7 points) Methyl chloride at 373 K (100 C) has the following virial coeﬃcients B =-242 . 5cm 3 / mol , C = 25 . 2 × 10 3 cm 6 mol-2 . Calculate the work of an isothermal reversible compression of 1 mole from 100 kpa to 5 Mpa. (a) Use the virial equation in volume Z = 1 + B V + C V 2 (b) Use the pressure variant of the virial equation Z = 1 + B P + c p 2 B = B RT , C = C-B 2 ( RT ) 2...
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