Solved: A gas expands in volume from 26.7 mL to 89.3 mL at

Step 1 of 3

Given:

Initial volume \(\left(\mathrm{V}_{\text {intial }}\right)=26.7 \mathrm{~mL}\)

Final volume \(\left(\mathrm{V}_{\text {final }}\right)=89.3 \mathrm{~mL}\)

(a) Here, we are asked to calculate the work done (in joules) if gas expands against a vacuum

Because the external pressure is zero, no work is done in the expansion.

The work done (w) is calculated using the formula shown below:

\(\mathrm{w}=-\mathrm{P} \Delta \mathrm{V}\)

Where P = pressure

\(\Delta \mathrm{V}=\mathrm{V}_{\text {final }}-\mathrm{V}_{\text {intial }}\)

\(\begin{aligned} \Delta \mathrm{V} & =89.3 \mathrm{~mL}-26.7 \mathrm{~mL} \\ & =62.6 \mathrm{~mL} \end{aligned}\)

Now,

\(\begin{aligned} \mathrm{w} & =-0 \times 62.6 \\ & =0 \end{aligned}\)

Hence, the work done against a vacuum is \(0 J\).