Final answer:
The adiabatic and quasi-static expansion of a gas in a cylindrical closed container involves plotting the path in the pV plane, calculating the work done by the gas, and finding the change in internal energy of the gas using the first law of thermodynamics.
Step-by-step explanation:
The adiabatic and quasi-static expansion of a gas in a cylindrical closed container from state A (3 MPa, 2 L) to state B (6 L) along the path 1.8pV=constant can be understood by plotting the path in the pV plane. The graph will show a curve that starts at point A and ends at point B, with the volume increasing and the pressure decreasing. The amount of work done by the gas during this process can be calculated using the formula:
Work = ∫ P dV, where P is the pressure and dV is the change in volume. In this case, the work done by the gas is the area under the curve on the pV plot.
The change in internal energy of the gas during the process can be found using the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added or removed from the system, and W is the work done by the gas. Since the process is adiabatic (Q=0), the change in internal energy is equal to the negative of the work done by the gas.