We’re being asked to **calculate the final volume** for a system if it **expands** from a volume of **51.1 mL** against a constant pressure of **783 torr**, doing **137.7 J** of work in the process.

Recall that ** work (w)** is given by:

$\overline{){\mathbf{w}}{\mathbf{=}}{\mathbf{-}}{\mathbf{P\Delta V}}}$

where:

**P** = pressure (in atm)

**ΔV** = V_{final} – V_{initial} = change in volume (in L)

Also note that if work is:

• **(+)**: work is done by the surroundings to the system *(compression)*

• **(–)**: work is done by the system to the surroundings *(expansion)*

A sample of gas occupies a volume of 51.1 mL. As it expands, it does 137.7 J of work on its surroundings at a constant pressure of 783 torr.

What is the final volume of the gas?

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