Question

A certain fuid at 10 bar is contained in a cylinder behind a piston the initial volume being 0.05m. Calculate the work done by the fuld when it expends reversibly) At constant pressure to a final volume of 0.2 m. ii) According to a linear law to a final volume of 0.2m '. & a final pressure of 2 bar. iii) According to a law (PV - constant) to a final volume of 0.1 m IV) According to a law (P. V3 = constant) to a final volume or 0.063 V) According to a law (P = (A / V2) ) - (B / V)) to a final volume of 0.1 m & final pressure of l bar where A, B are constants. Sketch all processes on (p - v) diagram

Answer 1

i) $W=p\Delta V=1000000\cdot(0.2-0.05)=150(kJ)$

ii) $W=\frac{(200000+1000000)\cdot0.15}{2}=90(kJ)$

iii) $W=p_1V_1\ln\frac{V_2}{V_1}=1000000\cdot0.05\cdot\ln\frac{0.1}{0.05}=34.7(kJ)$

iv) $W=\frac{1000000\cdot0.05}{3-1}(1-(\frac{0.05}{0.063})^{3-1})=9253(J)$

v) $W=\int pdV=\int(a/V^2-b/V)dV=10a-0.6931b.$

From the initial conditions $a=4000$ and $b=30000$.

So, $W=10\cdot4000-0.6913\cdot30000=19200(J)$.