An ideal gas is initially at is expanded to and then compressed adiabatically to the same volume and pressure . If is the net work done by the gas in complete process which of the following is true [2004]

Question

An ideal gas is initially at $P_{1}, V_{1}$ is expanded to $P_{2}, V_{2}$ and then compressed adiabatically to the same volume $V_{1}$ and pressure $P_{3}$ . If $W$ is the net work done by the gas in complete process which of the following is true [2004]

Smart Achievers · Accepted Answer

(2)

In the first process $W_{A B}$ is +ve as $P_{2}, V_{2}$ is positive.

In the second process $W_{B C}$ is $-$ ve as $Δ V$ is $-$ ve and area under the curve of second process is more.

$∴$ $Net Work < 0$ and also $P_{3} > P_{1}$

Solution

Q.
An ideal gas is initially at $P_{1}, V_{1}$ is expanded to $P_{2}, V_{2}$ and then compressed adiabatically to the same volume $V_{1}$ and pressure $P_{3}$ . If $W$ is the net work done by the gas in complete process which of the following is true [2004]

1 $W > 0; P_{3} > P_{1}$

2 $W < 0; P_{3} > P_{1}$

3 $W > 0; P_{3} < P_{1}$

4 $W < 0; P_{3} < P_{1}$

Ans.
(2)

In the first process $W_{A B}$ is +ve as $Δ V$ is positive.

In the second process $W_{B C}$ is $-$ ve as $Δ V$ is $-$ ve and area under the curve of second process is more.

$∴$ $Net Work < 0$ and also $P_{3} > P_{1}$

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Solution

Q. An ideal gas is initially at P1,V1 is expanded to P2,V2 and then compressed adiabatically to the same volume V1 and pressure P3. If W is the net work done by the gas in complete process which of the following is true [2004]

1 W>0; P3>P1

2 W<0; P3>P1

3 W>0; P3<P1

4 W<0; P3<P1

Ans. (2) In the first process WAB is +ve as ΔV is positive. In the second process WBC is -ve as ΔV is -ve and area under the curve of second process is more. ∴ Net Work<0 and also P3>P1