Assignment On Energy Balance Equation

MAE 204 Fall 2019 HW #6
Due at 4:00pm on 10/8/19. Turn in during lecture or to Jarvis 326.
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Problem 1 (15 pts)
Consider air being compressed in a closed piston-cylinder from an initial specific
volume of 1 m3/kg and 100 kPa to 1 MPa. Assume that specific heats vary with
temperature.
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a) Draw a schematic of the process, state appropriate assumptions, and write the
energy balance expression using the assumptions.
The following air standard-assumptions are made:
I. The liquid used is air
II. Ideal gas is used in the system
III. It’s a assume that the process used is reversible
The Energy balance equation is shown bellow
∆ U =−∆ KE + ∆ PE=Q−W
Q= heat transfer to the system
Air
Piston
System
Boundary
Parta
Air
Piston System
boundary
Partb

W=work done
∆ U =change of internal enegy
b) Determine the work into the system and heat out of the system, both in kJ/kg,
assuming the process is isothermal.
W=∫
1
2
pdv=¿∫
1
2
c
v dv= p 1 v 1 ln ( v 2
v 1 ) n=1¿
W=p1v1ln ( v 2
v 1 ¿
=100* 1ln ( 0.1
1 ¿=-230.259kj/kg
Work output is equal to heat out of the system
W¿ p 2 v 2 ln ( v 1
v 2 )=1000∗1 ln ( 1
0.1 )=230.259 kj/ kg