Answer :
Final answer:
The work done when a cylinder equipped with a piston expands from an initial volume of 477 ml to a final volume of 831 ml against an external pressure of 692 mmHg is calculated to be approximately 32.7 J. However, this calculated work does not match any of the provided options, indicating a potential error in the question's data or given options.
Explanation:
To determine the work done when a cylinder equipped with a piston expands from an initial volume of 477 ml to a final volume of 831 ml against an external pressure of 692 mmHg, we use the formula for work done by a gas at constant pressure: W = -P ∆V, where 'W' is work, 'P' is pressure, and '∆V' is the change in volume. First, we need to convert the external pressure to pascals (1 mmHg = 133.322 Pa), and volumes to cubic meters (1 mL = 1e-6 m³). The change in volume is (831-477) mL = 354 mL = 354e-6 m³. The external pressure is 692 mmHg = 692 × 133.322 Pa = 92281.104 Pa. Now we calculate the work:
W = -(92281.104 Pa) × (354e-6 m³)
W = -32.663568416 J
Since we want the answer in joules, we need to convert this to kilojoules by dividing by 1000, which yields approximately -32.7 J. However, we express work done by the system on its surroundings as negative, so the magnitude of work done is 32.7 J. This number does not match any of the options provided, suggesting that there could be a mistake in the data provided in the question or in the options.
