Solved Problems on Thermodynamics - Assignment 7 | ME 201, Assignments of Thermodynamics

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ME

Homework #7 Solutions

TA: Saeed Jahangirian

ME201 Homework #7 Solutions 7 Argon gas expands in a turbine. The exit temperature of the argon for a power output of 250 kW is to be determined. Assumptions | This 1s a steady-flow process since there 1s no change with time. 2 Potential energy changes are negligible. 3 The device is adiabatic and thus heat transfer is negligible. 4 Argon is an ideal gas with constant specific heats. Properties The gas constant of Ar is R= 0.2081 kPam'/kg.K. The constant pressure specific heat of Ar is ¢p = 0.5203 kI/keg-°C (Table A-2a) Analysis There is only one inlet and one exit, and thus i, = rizy = rir. The inlet specific volume of argon and its mass flow rate are in. cha) v= PA — (0.2081 kPa ong KF23K) _ 9 167 2p d=60.em! R 900 kPa P, =900 kPa Thus 7, = 450°C V, = 80 ms sn = Ly, = [0.006 nx? 80 m/s) = 2.874 kpis 4) O167m ke" We take the turbine as the system, which is a control volume since mass crosses the boundary. The energy balance for this steady-flow system can be expressed in the rate form as 70 (Heady) ig Rate of change in intemal, kmetic, ‘by heat, work, and ma: potential, ete. enerzies 150 kPa 150 m/s E,, = £, win (It, + 12) = Wegy + 0 Ity + Wea = nail Ity — Ty + Substituting. | 150 m/s)? — (80 m/s)? [ 250 kI/s =-(2.874 ko/s)| (0.5203 Ttke-* CMT, —450° Cy = G92 mvs) — GO mis) | 2 It yields T, = 267.3°C