Answer to Question #128832 in Mechanics | Relativity for Ariyo Emmanuel

Question #128832
1 kg of a fluid is compressed reversibly according to a law pv = 0.25, where p is in bar and v is in m3/kg. The final volume is one-fourth of the initial volume. Calculate the work done on the fluid and sketch the process on a p-v diagram.
Expert's answer

The work that it done by fluid is an integral under the curve pV=0.25 in (p,V) coordinates. According to the task, the fluid is compressed, so the work is done on fluid (has minus sign):

"W = -\\int_{V_1}^{V_2} pdV =\\int_{V_2}^{V_1} pdV"

from a low of fluid compression we can find "pV = 0.25 \\Rightarrow p = \\frac{0.25}{V}*10^5" (Pa). The multiplier "10^5" appeared because we have converted bar to Pa (SI units), 1 bar = "10^5" Pa. Also, we know that "V_2 = 0.25 V_1" . Now we can calculate the integral:

"W = \\int_{0.25V_1}^{V_1} \\frac{0.25*10^5}{V}dV = 0.25*10^5 ln (\\frac{V_1}{0.25V_1})=0.25*10^5 ln4 = 34 657" J "\\approx 34.7" kJ

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31.03.21, 02:47

Thank you, it was really helpful because i spent time trying to solve it but after seeing this solution all my doubts are gone.

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