A certain gas is isothermally compressed to ((1)/(3))^ rd of its...

For an isothermal process, the isothermal bulk modulus equals the gas pressure:
$B_T = -V\dfrac{dP}{dV}$

Since $PV = \text{constant}$, differentiating gives $P\,dV + V\,dP = 0$, so $\dfrac{dP}{dV} = -\dfrac{P}{V}$, which yields $B_T = P$.

Therefore, the initial pressure is:
$P_o = 3 \times 10^5\text{ N/m}^2$

Volumes:
$V_o = 3\text{ L} = 3 \times 10^{-3}\text{ m}^3$
$V_f = \dfrac{1}{3}V_o = 10^{-3}\text{ m}^3$

Work done on the gas during an isothermal compression:
$W_{\text{on}} = -W_{\text{by}} = -P_o V_o \ln\left(\dfrac{V_f}{V_o}\right) = P_o V_o \ln\left(\dfrac{V_o}{V_f}\right)$

$W_{\text{on}} = (3 \times 10^5)(3 \times 10^{-3})\ln 3$

$W_{\text{on}} = 900 \ln 3\text{ J}$

Using $\ln 3 \approx 1.0986$:
$W_{\text{on}} \approx 900 \times 1.0986 \approx 988.74\text{ J}$

Rounded to the nearest integer:
$W_{\text{on}} \approx 989\text{ J}$

Hence, the work done on the gas is approximately $989\text{ J}$.