A certain gas is isothermally compressed to \(\left(\dfrac{1}{3}\right)^{rd}\) of its initial volume (\(V_o = 3\) litre) by applying required pressure. If the bulk modulus of the gas is \(3 \times 10^5\) N/m\(^2\), the magnitude of work done on the gas is _______ J.

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 \(989\text{ J}\).