A horizonal piston-cylinder arrangement is placed in a constant temperature bath.The piston slides in the cylinder with negligible friction, and an external force holds it in place against an initial gas pressure of 14 bar.The initial gas volume is 0.03 m^3 (a)The external force on the piston is reduced gradually, allowing the gas to expand until its volume doubles.Calculate the work done by the gas in moving the external force. (b)How much work would be done if the same expansion is carried out by removing a part of the external force suddenly.Also calculate % efficiency of this process as compared with the reversible process (%of reversible work). Take ln2=0.7 Report your answer as (% efficiency xx 0.7).

A horizonal piston-cylinder arrangement is placed in a constant temper

1.	A horizonal piston-cylinder arrangement is placed in a constant temperature bath.The piston slides in the cylinder with negligible friction, and an external force holds it in place against an initial gas pressure of 14 bar.The initial gas volume is 0.03 m^3 (a)The external force on the piston is reduced gradually, allowing the gas to expand until its volume doubles.Calculate the work done by the gas in moving the external force. (b)How much work would be done if the same expansion is carried out by removing a part of the external force suddenly.Also calculate % efficiency of this process as compared with the reversible process (%of reversible work). Take ln2=0.7 Report your answer as (% efficiency xx 0.7).
Answer» SOLUTION :(a)W=-nRT In `V_2/V_1` `W=-P_1V_1` In `V_2/V_1=-14xx0.03"In"0.06/0.03"bar"m^3= -14xx0.7xx0.03= -0.294 "bar" m^3` (B)`P_1V_1=P_2V_2` `:. P_2=(P_1V_1)/V_2=(14xx0.03)/(0.06)=7` bar `:. W=-P_(EXT)(V_2-V_1)=-7(0.06-0.03)=-7xx0.03= -0.21 "bar"m^3` Efficiency `=0.21/0.294=71.43%`