D

Step 1: Let's analyze the isothermal process for the nitrogen gas. Since it is isothermal, we can apply the first law of thermodynamics and the properties of an ideal gas.
In an isothermal process for an ideal gas, the heat added to the system ($Q$) is equal to the work done by the gas ($W$), i.e.,
$$ Q = W $$
For this process, we know that:
$$ W = Q = 11300 ext{ J} $$
Step 2: Now, let's consider the adiabatic process that follows. In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). For an ideal diatomic gas like nitrogen, we can use the adiabatic relations to derive the work done.
When the gas expands adiabatically, the work done ($W_{adiabatic}$) can be represented by the equation:
$$ W_{adiabatic} = rac{P_{initial} (V_{final} - V_{initial})}{ ext{specific heat ratio}} $$
However, instead of calculating the exact values for pressure and volume during the adiabatic transition, we can understand that for the entire process (isothermal followed by adiabatic expansion) the total work done ($W_{total}$) is the sum of work done during both processes.
In this case, since the expansion is finite (the volume becomes four times the initial), the work done during the adiabatic expansion will physically return to the system as an energy exchange.
Step 3: To find the total work done on the system, using the efficiency of the process and the boundaries we established, we can reason that the work done during the entire transformation including the heat exchanged is approximately the heat added in the isothermal process, given the lack of additional information for the specific adiabatic expansion.
Thus, we conclude the work done is:
$$ W_{total} = 11300 ext{ J} $$
Therefore, in terms of options, if the total work performed is specifically observed, the best-answer option reflecting this value would be directly referenced in relation to our isothermal heat addition and gas expansion.
Hence, the work done by the gas is 11300 J or option D.
Therefore, the correct response is: D.