A piston–cylinder device initially contains 0.4 m^3 of air at 100 kPa and 80°C.?
A piston–cylinder device initially contains 0.4 m^3 of air at 100 kPa and 80°C. The air is now compressed to 0.1 m^3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process.
Hint: You need to integrate over the volume first before calculating the work done.
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The process is isothermal so
PV = constant = C = p1*v1 = 40000
now work done in closed system (such as piston cylinder) = p dv
dw = p dv
dw = C/V dv
Now integrating this
W = C integral (1/V) dv to limits v1 to v2
W = C ln(V2/V1)
W = 40000*ln(0.1/0.4) ,ln is log to base e
W = -55.451 kW
Negative shows work is done on system.