Question

Air contained in an insulated piston-cylinder assembly, initially at 8 bar, 377 °C and a volume of 0.60 m3, expands to a pressure of 2 bar. Model the air as an ideal gas with constant specific heats. a. Sketch process on a p-v and T-s diagram. Clearly indicate accessible states allowed by 2nd Law. T V b. Determine the maximum work of the expanding air (both magnitude and direction). Justify using the laws of thermodynamics. c. If the actual work is only 90% of the maximum calculated in part (b), how much entropy was produced? d. If the piston were not insulated, how would cooling effect the accessible states? Show on property diagrams in part (a) and justify answer in terms of 2nd Law.

Answer 1

For the air contained insulated piston - Cylinder assembly Initial pressure, P, = 8 bar, Initial temperature, Ti = 377°C 65ok - Initial volume Vi O: 60 m3 Final pressure P₂ = 2 bar adaiabetic 1 ire is expanded in Process rocess. The ges From the thermodynamic relation since it is a isoleted au= agt w [ Here oo=0 system ou W

Now from the relation - -- P, الدا = P2 V2² 1² Vi (P2) V2 114 for Ideal Ideal (here 2= gus Yory 0.60 ( 8 2 1.615 m3 The final $ volume +3 1.615X10 L is :15% = 1615 m3 final . The demperature is V2 T/ 2 x 1.65 x 163 8.314 x10-5 R. *241 >-1 T2 = T st 1.4-) 650 0 '60 115 437.42 k TA P LI v

MO maximum work done Wmas 2 nR(T2-T) 1-3 = 80314 ( 437.42-650) (-114) = +4418.345 J the tre s Bigon indicates the the worke is done by gas, The magnitude of the maximum wook done 44 18.345J and the direction is @ upword to the piston, دار Hence for an isoleted systed system os gas expansion the internal temperature of an ideal decreases, due to work done gas is done -the o internal em energy of the by gas system, (es 90% of go% of the maximum work - E 4418.345 x 90 100 = 3976.51J that This means at the to time of expansin some is takon from the outsid of the system ine. temperature Iz is change. i. 397651 = R( Tz-650) (-1.4) l! wy 458.68 K

It means that the final temporeture in å norreased. The entropy produced des T. there do (4418:341-3976151) J 441.833 ir produced 441-83 J •ds= entropy 458.68k = 0.863 J K-1 d) If the påston is insulated the beat will be not exchange due to expansion of gas. So in that Case not occur due to the Cooling effect is In this Case the required taken from the is process of isothermic expansion. temperature for q expansion of gas not affected due to this Surrounding so tomprrature not insulated piston system, so temporatiune remain same, PA T isothermic cuore. AN

T TX for isothermal pávcess for insulated pistor S S not insulated og piston system entropy in mases due to expansion for the