Energy is added to a piston-cylinder arrangement, and the piston is withdrawn in such a way that the quantity PV remains constant. The initial pressure and volume are 200 kPa and 2 m 3 , respectively. If the final pressure is 100 kPa, calculate the work done by the gas on the piston.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. W 1–2 = 
dV = 
dV
where we have used PV = C. To calculate the work we must find C and V 2 . The constant C is found from
C = P 1 V 1 = (200) (2) = 400 kJ
To find V 2 we use P 2 V 2 = P 1 V 1 , which is, of course, the equation that would result from an isothermal process (constant temperature) involving an ideal gas. This can be written as
V 2 = 
= 
= 4m 3 Finally,
W 1–2 = 
dV = 400 ln 
= 277 kJ
This is positive, since work is done during the expansion process by the system (the gas contained in the cylinder).
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