Question

1Kg of a fluid iss compressed reversibly according to a law pv=0.25 where p is in bar v is in m^3/Kg.The final volume is 1/4 of the initial volume.calculate the work done on the fluid and sketch the P-V diagram

Answer 1

Answer on Question #58674-Engineering-Mechanical Engineering

1Kg of a fluid is compressed reversibly according to a law $pv = 0.25$ where $p$ is in bar $v$ is in $m^{\wedge}3 / Kg$ . The final volume is 1/4 of the initial volume. Calculate the work done on the fluid and sketch the P-V diagram

Solution

The work done on the fluid is

$$W = - \int_ {V _ {1}} ^ {V _ {2}} p d V = \int_ {V _ {2}} ^ {V _ {1}} p d V;$$ $$p v = 0. 2 5 \rightarrow p = \frac {0 . 2 5}{V}.$$ $$1 b a r = 1 0 ^ {5} P a$$ $$W = \int_ {V _ {2}} ^ {V _ {1}} \frac {0 . 2 5 \cdot 1 0 ^ {5}}{V} d V = 0. 2 5 \cdot 1 0 ^ {5} \ln \left(\frac {V _ {1}}{V _ {2}}\right) = 0. 2 5 \cdot 1 0 ^ {5} \ln \left(\frac {1}{1 / 4}\right) = 3 4 6 6 0 J.$$

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