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-1-T-1-T-2-2-T-3-gt-T-1-3-

Question Number 24263 by Tinkutara last updated on 14/Nov/17

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 ?

(1) T_{1} = T_{2}

(2) T_{3} > T_{1}

(3) w_{isothermal} > w_{adiabatic}

(3) Δ U_{isothermal} > Δ U_{adiabatic}

Commented by Tinkutara last updated on 14/Nov/17

Commented by ajfour last updated on 14/Nov/17

V_{2} = \frac{{n R T}_{2}}{P_{2}} = \frac{{n R T}_{3}}{P_{3}}

a s P_{2} > P_{3} w e c a n i n f e r

T_{2} > T_{3} .

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

W_{i s o t h e r m a l (b y g a s)} > W_{a d i a b a t i c (b y g a s)}

(H e n c e Q_{i s o t h e r m a l} > Q_{a d i a b a t i c},

i f w e g o u s e Q_{t o g a s} = W_{b y g a s} + △ U_{o f g a s}) .

s o (1), (3), (4) .

Commented by Tinkutara last updated on 15/Nov/17

But please recheck (2) option, is it

true or not ?

Commented by ajfour last updated on 15/Nov/17

T_{1} = T_{2} a n d P_{2} > P_{3}

A l s o \frac{n R}{V_{2}} = \frac{P_{2}}{T_{2}} = \frac{P_{3}}{T_{3}}

\Rightarrow T_{3} = T_{2} (\frac{P_{3}}{P_{2}}) < T_{2}

S o T_{3} < T_{1} .

Commented by Tinkutara last updated on 15/Nov/17

Thank you very much Sir!