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2300_hw_13_sol

# 2300_hw_13_sol - 7-88 An insulated cylinder initially...

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7-88 An insulated cylinder initially contains air at a specified state. A resistance heater inside the cylinder is turned on, and air is heated for 15 min at constant pressure. The entropy change of air during this process is to be determined for the cases of constant and variable specific heats. Assumptions At specified conditions, air can be treated as an ideal gas. Properties The gas constant of air is R = 0.287 kJ/kg.K (Table A-1). Analysis The mass of the air and the electrical work done during this process are ( ) ( ) ( ) ( ) ( )( ) kJ 180 s 60 15 kJ/s 0.2 kg 0.4325 K 290 K /kg m kPa 0.287 m 0.3 kPa 120 in e, in e, 3 3 1 1 1 = = D = = = = t W W RT P m & V The energy balance for this stationary closed system can be expressed as ) ( ) ( 1 2 1 2 in e, out b, in e, energies etc. potential, kinetic, internal, in Change system mass and work, heat, by nsfer energy tra Net out in T T c h h m W U W W E E E p - @ - = D = - D = - 43 42 1 43 42 1 since D U + W b = D H during a constant pressure quasi-equilibrium process. ( a ) Using a constant c p value at the anticipated average temperature of 450 K, the final temperature becomes Thus, ( )( ) K 698 K kJ/kg 1.02 kg 0.4325 kJ 180 K 290 in e, 1 2 = + = + = p mc W T T Then the entropy change becomes ( ) ( )( ) kJ/K 0.387 K 290 K 698 ln K kJ/kg 1.020 kg 0.4325 ln ln ln 1 2 avg , 0 1 2 1 2 avg , 1 2 sys = = = - = - = D T T mc P P R T T c m s s m S p p ( b ) Assuming variable specific heats, ( ) kJ/kg 706.34 kg 0.4325 kJ 180 kJ/kg 290.16 in e, 1 2 1 2 in e, = + = + = - = m W h h h h m W From the air table (Table A-17, we read s 2 o = 2.5628 kJ/kg·K corresponding to this h 2 value. Then, ( ) ( )( ) kJ/K 0.387 K kJ/kg 1.66802 2.5628 kg 0.4325 ln 1 2 0 1 2 1 2 sys = - = - = + - = D o o o o s s m P P R s s m S 7-92 One side of a partitioned insulated rigid tank contains an ideal gas at a specified temperature and pressure while the other side is evacuated. The partition is removed, and the gas fills the entire tank. The total entropy change during this process is to be

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2300_hw_13_sol - 7-88 An insulated cylinder initially...

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