Question

Consider an ideal gas that occupies $2.50d{m}^3$ at a pressure of 3.00 bar. If the gas is compressed isothermally at a constant pressure $p_{ext},$ so that the final volume is $0.500d{m}^3,$ calculate the smallest possible value of $p_{ext}$ and the work done using $p_{ext}$.

• A. 20 bar and 100 J
• B. 15 bar and 3000 J
• C. 30 bar and 150 J
• D. 10 bar and 375 J

Answer 1

The correct option is B 15 bar and 3000 J

For a compression to occur, $p_{ext}$ must be at least as large as the final pressure of the gas. The final pressure of the gas is
$P_f=\frac{P_i{V}_i}{V_f}=\frac{\left(3.0bar\right)\left(2.50d{m}^3\right)}{0.50d{m}^3}$
This is the smallest possible value of $p_{ext}$ that can be applied to compress the gas isothermally from $2.50d{m}^3$ to $0.5d{m}^3.$ The work done involving the value of $p_{ext}$ is
$W=-p_{ext}△V=\left(15bar\right)\left(2d{m}^3\right)=30d{m}^{3}bar$
$=\left(30d{m}^{3}bar\right)\left({10}^{-3}{m}^{3}d{m}^{-3}\right)\left({10}^5\right)Paba{r}^{-1}$
$=3000Pa.m^3=3000J.$