Question
An ideal gas occuping a volume of $$2d{m^3}$$ and a pressure of $$5\,bar$$ undergoes isothermal and irreversible expansion against external pressure of $$1\,bar$$ The final volume of the system and the work involved in the process is
A.
$$10\,d{m^3},1000\,J$$
B.
$$8\,d{m^3},\, - 800\,J$$
C.
$$10\,d{m^3}, - 800\,J$$
D.
$$10\,d{m^3}, - 1000\,J$$
Answer :
$$10\,d{m^3}, - 800\,J$$
Solution :
$$\eqalign{
& {P_1}{V_1} = {P_2}{V_2} \cr
& \therefore \,\,V = \frac{{5\,bar \times 2d{m^3}}}{{1\,bar}} \cr
& = 10\,d{m^3} \cr
& {\text{Work,}}\,\,W = - {P_{ext}}\left( {\left( {{V_{final}} - {V_{initial}}} \right.} \right) \cr
& = - 1\,bar\left( {10 - 2} \right) \cr
& = - 1 \times {10^5}Pa \times 8 \times {10^{ - 3}}{m^3} \cr
& = - 800\,J \cr} $$