A system consisting of 1 mole of an ideal gas undergoes an isothermal expansion at `25^(@)` from 1.0 bar to a lower pressure while generating 100 J of work. What is the final pressure of the system if the external pressure of the system is constant of 0.1 bar?

Options

A. 1.23 bar
B. 0.712 bar
C. 0.958 bar
D. 0.664 bar

Answer

B

Explanation

Given, `p_(ext)=0.1," bar ",R=8.314JK^(-1)mol^(-1),T=298K,`
`p_(1)=1" bar",p_(2)=?`
`W=-p_(ext)(V_(2)-V_(1))`
`=-p_(ext)((nRT)/(p_(2))-(nRT)/(p_(1)))`
`=-nRT" "p_(ext)((1)/(p_(2))-(1)/(p_(1)))`
or `-100=-1xx8.314xx298xx0.1((1)/(p_(2))-(1)/(1))`
`therefore p_(2)=0.712` bar