Question

Air at 200kPa, 30°C is contained in a cylinder behind a piston with initial volume of 0.1 m3. The inside pressure balance ambient pressure of 100 kPa plus an external imposed force that proportional to V3, Now heat is transfer to the systēm to final pressure of 225 kPa. Find the work done for this process

Answer 1

$p=p_0+CV^3$

$200000=100000+C\cdot 0.1^3 \to C=100000000$

$225000=100000+100000000\cdot V^3_2 \to V_2=0.108 m^3$

$W_{12}=\int pdV=\int (p_0+CV^3)dV=$

$=p_0(V_2-V_1)+\frac{C}{4}(V^4_2-V^4_1)=$

$=100000\cdot(0.108-0.1)+\frac{100000000}{4}\cdot(0.108^4-0.1^4)\approx 1701 J$