Calorimetry....

Question

A sample of flammable liquid is placed into an enclosed cylinder which is then fitted with a movable piston. Initially the cylinder contains a volume of 7.30 L. The sample is ignited producing gas and releasing 534.4 J of energy. To what volume will the cylinder expand to if it must expand against a pressure of 733.7 mmHg. Assume all the energy released is converted to work used to push the piston? 

Answer 1

Since the piston is moving against the atmospheric pressure, work is being done BY THE SYSTEM on the surroundings, so the work will have a negative sign.

w = -P∆V

w = work = -534.4 J

P = pressure = 733.7 mm Hg x 1 atm / 760 mm Hg = 0.965 atm

∆V = change in volume in L = ?

Solve for ∆V (recall that 1 Latm = 101.325 J)

-534.4 J x 1 Latm / 101.325 J = -5.27 Latm

∆V = -5.27 Latm / -0.965 atm

∆V = 5.46 L

So, the cylinder would have to expand to a volume of 7.30 L + 5.46 L = 12.8 L