The figure shows two paths through which a gas can be taken from state A to state B. If the ratio of work done by the gas in the two paths is x / y, then find (x+y).

Question

The figure shows two paths through which a gas can be taken from state A to state B. If the ratio of work done by the gas in the two paths is x / y, then find (x+y). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Δ WA B= Area under A arrow B bounded by volume axis. =10 × 103(25-10) × 10-6 +(1/2)(25-10) × 10-6 × 20 × 103 =0.15+0.15=0.3 J In path A arrow C arrow B, Δ WA C B=30 × 103(25-10) × 10-6 =0.45 J

Q. The figure shows two paths through which a gas can be taken from state $A$ to state $B$ . If the ratio of work done by the gas in the two paths is $x / y$ , then find $(x + y)$ .

$Δ W_{A B} =$ Area under $A \to B$ bounded by volume axis.
$= 10 \times 1 0^{3} (25 - 10) \times 1 0^{- 6} + \frac{1}{2} (25 - 10) \times 1 0^{- 6} \times 20 \times 1 0^{3}$
$= 0.15 + 0.15 = 0.3 J$
In path $A \to C \to B$ ,
$Δ W_{A CB} = 30 \times 1 0^{3} (25 - 10) \times 1 0^{- 6}$
$= 0.45 J$

Q. The figure shows two paths through which a gas can be taken from state A to state B. If the ratio of work done by the gas in the two paths is x/y, then find (x+y).

ΔWAB​= Area under A→B bounded by volume axis. =10×103(25−10)×10−6+21​(25−10)×10−6×20×103 =0.15+0.15=0.3J In path A→C→B, ΔWACB​=30×103(25−10)×10−6 =0.45J

Q. The figure shows two paths through which a gas can be taken from state $A$ to state $B$ . If the ratio of work done by the gas in the two paths is $x / y$ , then find $(x + y)$ .

$Δ W_{A B} =$ Area under $A \to B$ bounded by volume axis.
$= 10 \times 1 0^{3} (25 - 10) \times 1 0^{- 6} + \frac{1}{2} (25 - 10) \times 1 0^{- 6} \times 20 \times 1 0^{3}$
$= 0.15 + 0.15 = 0.3 J$
In path $A \to C \to B$ ,
$Δ W_{A CB} = 30 \times 1 0^{3} (25 - 10) \times 1 0^{- 6}$
$= 0.45 J$