Final answer:
Option b) 40 L.
The final volume of the gas after performing 1.7 kJ of work on its container is calculated using the work energy theorem and the ideal gas law. Assuming constant temperature and pressure during the expansion, the final volume is found to be approximately 40 L.
Step-by-step explanation:
To solve for the final volume of the ideal gas after expansion, we need to use the work energy theorem W = -PΔV (where the work is done by the gas on the surroundings) and the ideal gas law PV = nRT.
Given that the work, W, done by the gas is 1.7 kJ (which is 1700 J since 1 kJ = 1000 J), and the temperature, T, is constant at 280 K, we can write:
- W = -PΔV = -1700 J
- PV = nRT (initial and final states)
- PiVi = PfVf
- Pi = nRTi / Vi
- Pf = nRTf / Vf
Assuming the pressure remains constant during the expansion (isobaric process), Pi = Pf = P and we can cancel it out in the work equation. With Pi = nRTi / Vi, we have:
-1700 J = -(nRT/Vi) × (Vf - Vi)
Substitute the given values (n = 1.4 moles, R = 8.314 J/(mol · K), T = 280 K, Vi = 34 L):
-1700 J = -(1.4 moles × 8.314 J/(mol · K) × 280 K / 34 L) × (Vf - 34 L)
After calculating the pressure and rearranging the equation to solve for Vf, you will find that the final volume of the gas is approximately 40L, which corresponds to option b).