Question

To a closed system, 150kJ of work is supplied. If the initial volume is 1.6m^3 and the pressure of the system changes as P=(8+4v) P in bar and v in m^3, determine the fluid volume and pressure of the system

Answer 1

The work supplied to a close system is given by:

$A=\int_{v_0}^{v}{pdv}=\int_{v_0}^{v}{(8+4v)dv}=(8v+4v^2)|_{v_0}^{v}=2v^2+8v-2v_0^2-8v_0.$

Substitute:

$150\cdot10^{-2}=2v^2+8v-2\cdot1.6^2-8\cdot1.6;$

$2v^2+8v-19.42=0.$

The obtained quadratic equation has the only positive root $v=1.7027 m^3.$

The final pressure of the system equals to:

$P=8+4\cdot1.7027=14.811 bar.$