A certain gas is isothermally compressed to $$\left(\frac{1}{3}\right)^{rd}$$ of its initial volume ($$V_0 = 3$$ 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.

$$B = P = 3 \times 10^5 \text{ N/m}^2$$

$$W = -nRT \ln\left(\frac{V_f}{V_0}\right) = -PV_0 \ln\left(\frac{V_f}{V_0}\right)$$

$$\text{Work Done} = -PV_0 \ln\left(\frac{V_f}{V_0}\right)$$

$$\text{Work Done} = -(3 \times 10^5) \times (3 \times 10^{-3}) \times \ln\left(\frac{1}{3}\right)$$

$$\text{Work Done} = -900 \times (-\ln 3) = 900 \ln 3$$

$$\text{Magnitude of Work Done} = 900 \times 1.098612 \approx 988.75 \text{ J}$$

Rounding off to the nearest integer gives $$989 \text{ J}$$.