An ideal gas goes through the path 1-2-3-4 on a P - V diagram with 1 at ( 3 V 1 , P 1 ) , 2 at ( V 1 , P 1 ) , 3 at ( V 1 , 3 P 1 ) and 4 at ( 4 V 1 , 3 P 1 ) , each step being a strai

Question

An ideal gas goes through the path 1-2-3-4 on a $P$ - $V$ diagram with 1 at $(3 V_{1}, P_{1})$ , 2 at $(V_{1}, P_{1})$ , 3 at $(V_{1}, 3 P_{1})$ and 4 at $(4 V_{1}, 3 P_{1})$ , each step being a straight horizontal or vertical segment. Find the work done by the gas from 1 to 4 in units of $P_{1} V_{1}$ .

Answer:

7

Solution:

1 to 2: $P_{1} (V_{1} - 3 V_{1}) = - 2 P_{1} V_{1}$ . 2 to 3: no work. 3 to 4: $3 P_{1} (4 V_{1} - V_{1}) = 9 P_{1} V_{1}$ . Total = $7 P_{1} V_{1}$ .

TestHub · Accepted Answer

1 to 2: P 1 ​ ( V 1 ​ − 3 V 1 ​ ) = − 2 P 1 ​ V 1 ​ . 2 to 3: no work. 3 to 4: 3 P 1 ​ ( 4 V 1 ​ − V 1 ​ ) = 9 P 1 ​ V 1 ​ . Total = 7 P 1 ​ V 1 ​ .

Physics - Heat & Thermo Question with Solution | TestHub

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