Question

To a closed system 150 kJ of work is supplied. If the initial volume is 0.6 m³ and pressure of the system changes as p = 8 – 4V, where p is in bar and V is in m³, determine the final volume and pressure of the system

Answer 1

Amount of work supplied to a closed system = 150 kJ

Initial volume = 0.6 m³ 

Pressure-volume relationship, p = 8 – 4V

The work done during the process is given by

But this work is equal to – 150 × 10³ J as this work is supplied to the system.

∴ – 150 × 10³ = 10⁵[8V₂ – 2V₂² – 4.08]

or 2V₂² – 8V₂ + 2.58 = 0

Positive sign is incompatible with the present problem, therefore it is not considered

Final volume, V₂ = 0.354 m³.  

and, final pressure, p₂ = 8 – 4V = 8 – 4 × 0.354

= 6.584 bar = 6.584 × 10⁵ N/m² or Pa.