1.25 kg of a gas within a piston-cylinder assembly, undergoes an expansion from

Question

1.25 kg of a gas within a piston-cylinder assembly, undergoes an expansion from a volume of v1=0.1m3 to a volume of v2=0.3m3, through a polytropic process with n=1.25. It then undergoes a second expansion to a volume of v3=0.5m3, through a process where p=((0.05bar*m3)/v)+2bar. The changes in specific internal energy for the two expansions are u2-u1=-50kJ/kg, and u3-u2=-15kJ/kg.

Find p1,p2,p3(in bar), work of the fluid from 1 to 2(in kJ), and the net heat transfer from 1 to 2(in kJ).

(please show and explain all steps/work in answer)

Explanation / Answer

(second expansion) from p= 0.05/V + 2
at V2=0.3m3p2=2.17 bar

at V3=0.5m3p3=2.1 bar

first expansion undergoes the polytropic process, n=1.25 , PV1.25 = constant

p1(v1)1.25 = p2(v2)1.25        -> p1= 8.57 bar

work from 1->2 For polytropic process

w1->2= (p1V1-p2V2) / (n-1)           (p in kPa, 1 bar =101.3kPa)

w1->2=83.471 kJ/kg

W1->2=83.471*1.25 = 104.34 kJ

Q1->2 = m*u + W = 1.25*(-50) + 104.34 = 41.84 kJ (Heat into the system)

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