A sample of flammable liquid is placed into an enclosed cylinder which is then fitted with a movable piston. Initially the cylinder maintains a volume of 1.7 L. The sample is ignited producing gas and releasing 439.6 J of energy. To what volume will the cylinder expand to if it must expand against a pressure of 738.52 mmHg. Assume all the energy released is converted to work used to push the piston? Answer to 1 decimal space.

Concept of work :If we apply force on an object and if the object moves and changes it's position, then product of the force and the displacement of an object in the direction of applied force is called work.

Given,

Pressure= P= 738.52 mm Hg = 0.97 atm. (∵ 760 mm Hg = 1 atm)

Initial volume =V1= 1.7 L

Work done = W = 439.6 J

As we need our answer in litters ..

let's convert the work done into suitable units

∴work done = W = 4.26 L-atm (∵ 1 J = 101.3 L-atm)

As given all the energy is assumed to converted into work so we need not to worry About heat loss or entropy.

work done = pressure * difference in volume

W = PΔV

ΔV = 4.26÷ 0.97

∴ΔV = 4.38 LIt

There for, the volume expanded = 4.38 Lit

So, total volume = 4.38+ 1.7 = 6.08 Lit.

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