12.9 A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in Fig. (12.13)

 

Its volume is then reduced to the original value from E to F by an isobaric process. Calculate the total work done by the gas from D to E to F

<p>Total work done by the gas from D to E to F = Area of&nbsp;<span title="Click to copy mathml"><math><mo>? </mo><mi></mi><mi>D</mi><mi>E</mi><mi>F</mi></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></span>&nbsp;EF&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><mi>D</mi><mi>F</mi></math></span></p><p>Where DF = Change in pressure = 600 – 300 = 300 N/&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math></span></p><p>FE = change in volume = 5-2 = 3&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math></span></p><p>Area of&nbsp;<span title="Click to copy mathml"><math><mo>? </mo><mi></mi><mi>D</mi><mi>E</mi><mi>F</mi><mo>=</mo><mi></mi></math></span>&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mo>×</mo></math></span>&nbsp;3&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><mn>300</mn></math></span>&nbsp;= 450 J</p><p>Therefore work done by the gas from D to E to F is 450 J.</p>

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