The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

Options

A. `T_(1)=T_(2)`
B. `T_(3)gtT_(1)`
C. `w_("isothermal")gtw_("adiabatic")`
D. `DeltaU_("isothermal")gtDeltaU_("adiabatic")`

Answer

A, D

Explanation

For isothermal expansion, `DeltaT=`constant i.e. `T_(1)=T_(2)`
at const temperature, internal energy `(DeltaU)` of the system remains constant i.e.,
`DeltaU_("isothermal")=0`
Reversible expansion work=`-2.303nRT"log"(V_(2))/(V_(1))`
In adiabatic expansion, no heat is allowed to enter `w` is leave the system, hence `q = 0`
`DeltaE=q+w. :. q = 0`
`DeltaE=w`
In expansion, work is doen by the system, hence `w` is negative, accordingly, `DeltaE=-ve`, i.e.,
Internal energy decrease and therefore the temperature of the system falls.
Thus, `T_(3) lt T_(1)`
Thus, `DeltaU_("adiabatic")=-ve`
Thus, `DeltaU_("Isothermal") gt DeltaU_("adiabatic")`
`w_("adiabatic")=R/((gamma-1))(T_(2)-T_(1))`
Thus, Including sign,
`w_("isothermal") lt w_("adiabatic")`