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) gt T_(1)`
C. `w_("isothermal") gt w_("adiabatic")`
D. `DeltaU_("isothermal") gt DeltaU_("Adibatic")`

Answer

A, C, D

Explanation

(a) In isothermal process, temperature is constant, thereofore
`T_(1)=T_(2)`
(c) `w_("isothermal")gtw_("adiabatic")`
Area under curve is greater for isothermal process, than that for adiabatic process.
(d). `DeltaU_("isothermal")=0`
Fro adiabatic process:
`TV^(gamma-1)=`constant
`thereforeT_(1)V_(1)^(gamma-1)=T_(3)V_(3)^(gamma-1)`
`(T_(3))/(T_(1))=((V_(1))/(V_(3)))^(gamma-1)`
`T_(3) lt T_(1)` hence internal energy will decrease.
i.e., `DeltaU_("isothermal")gt DeltaU_("adiabatic")`