Final answer:
Calculation based on the first law of thermodynamics and properties of an ideal monatomic gas shows that the work done by the system is -1678.5 J, but this result does not match the answer choices provided. Therefore, the question cannot be answered with certainty given the current data and options.
Step-by-step explanation:
When 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, and its temperature rises by 10°C, the work done on the gas can be determined using the first law of thermodynamics. This law states that the change in the internal energy of a system (ΔU) is equal to the heat added to the system (Q) minus the work done by the system on its surroundings (W), which is ΔU = Q - W. For an ideal monatomic gas, the molar heat capacity at constant pressure (Cp) is 5/2 R, and at constant volume (Cv) is 3/2 R, where R is the universal gas constant. In this scenario, since the gas is heated at constant pressure, we use Cp. The change in internal energy can be calculated using the equation ΔU = n * Cp * ΔT, with n being the number of moles, and ΔT the change in temperature in kelvin.
ΔU for 10 mol of gas undergoing a 10°C (or 10 K) temperature increase at constant pressure is thus ΔU = 10 mol * 5/2 R * 10 K. Since R ≈ 8.314 J/(mol·K), we have ΔU = 10 * 5/2 * 8.314 * 10 J = 10 * 5 * 4.157 J = 2078.5 J. Considering that the heat added (Q) is 400 J, we can now find the work done by rearranging the first law to W = Q - ΔU. Therefore, W = 400 J - 2078.5 J = -1678.5 J. This negative sign indicates work was done by the system, not on it.
However, no option in the given answers fits the calculation (-1678.5 J), which suggests an error in the given options or the need for additional information to correctly answer the question. Therefore, with the provided information, a definitive answer cannot be given from the choices presented.