Final answer:
To determine the final volume of a diatomic gas expanded at constant pressure, we use the work formula W = PΔV and the relation Q = W for constant pressure processes. We find that the final volume is approximately 12.00 L after adding 400 J of heat to the gas at a constant pressure of 2.000 atm.
Step-by-step explanation:
To find the final volume of a diatomic gas after it has been heated and expanded against a constant pressure, we can use the first law of thermodynamics, which 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 (W).
For a constant pressure process, work done by the gas, W, is given by:
W = P ΔV
where P is the pressure and ΔV is the change in volume. Since we have a constant pressure of 2.000 atm and we're adding 400 J of heat, we need to convert the pressure from atm to J/L, using the factor 1 atm = 101.325 J/L. This gives us a pressure of 202.65 J/L.
We know that Q = W for a constant pressure process, so:
400.0 J = 202.65 J/L × ΔV
ΔV = 400.0 J / 202.65 J/L = 1.974 L
The initial volume was 10.00 L, so the final volume (V_final) is:
V_final = 10.00 L + 1.974 L = 11.974 L
Therefore, the final volume of the gas after heating is approximately 12.00 L. The closest answer choice to this calculated value is (a) 12.00 L.