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?

T_{1} = T_{2}

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T_{3} > T_{1}

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_{i s o t h e r m a l} >

_{a d i a b a t i c}

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Δ U_{i s o t h e r m a l} > Δ U_{a d i a b a t i c}

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Solution

The correct options are
A $T_{1} = T_{2}$
C W $_{i s o t h e r m a l} >$ W $_{a d i a b a t i c}$
D $Δ U_{i s o t h e r m a l} > Δ U_{a d i a b a t i c}$
(A) For an Isothermal process, the temperature is constant

$∴ T_{1} = T_{2}$

(B) Adiabatic process temp. decreases.
$∴ T_{3} < T_{1}$

(C) In $W_{i s o t h e r m a l}, Δ U = 0$ , so energy gets converted in to work done whereas for in the adiabatic process $Q = 0$

$∴ W_{i s o t h e r m a l} > W_{a d i a b a t i c}$ .

(D) For isothermal process change in internal energy is constant but not in the adiabatic process. Thus

$Δ U_{i s o t h e r m a l} = 0, Δ U_{a d i a b a t i c} = - v e$ , so

$∴ Δ U_{i s o t h e r m a l} > Δ U_{a d i a b a t i c}$

Hence, the correct options are $A,$ $C$ and $D$

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