The initial volume of the gas is 11 L, and the temperature is 273 K.
The given scenario involves an isothermal expansion of one mole of an ideal gas, during which it performs 2000 joules of work on the surroundings. For an isothermal process, the relationship between pressure (P), volume (V), and temperature (T) for an ideal gas is given by the equation PV=nRT, where n is the number of moles and R is the gas constant.
Given the final pressure and final volume, we can rearrange the ideal gas law to find the initial volume using the formula V_initial = nRT_initial/P_initial. Since the process is isothermal, the initial and final temperatures are the same, allowing us to solve for V_initial.
Simultaneously, the work done during the expansion (W) is given by W=−nRTln( V_final/V_initial). The negative sign is used because work is done by the system on the surroundings during expansion.
Given that W=2000 J and using the known values for n, R, and T, we can rearrange the work equation to solve for the initial volume. The resulting initial volume is 11 L. Therefore, the isothermal expansion began with an initial volume of 11 L, and the temperature of the gas is 273 K.