Rather harder: As in question 5, the external pressure is initially 1 × 105 Pa, but now this in increased instantaneously to 2 × 105 Pa. Suppose that the system’s final equilibrium state is that same as the final state of question 5. Assuming that the change of state takes place at constant temperature, is the change in state of the system quasistatic? How might you represent this change in state on a P, V diagram? How might you estimate the work done on the system by the surroundings? How does this answer compare to the answer to question 5?
For the system described in question 4, suppose that the external pressure is initially 1 × 105 Pa. If the external pressure is increased quasistatically to 2 × 105 Pa, what is the final equilibrium pressure of the system if the temperature of the system is maintained constant? What is the corresponding final volume? How much work is done on the system by the surroundings for the change from the system’s initial state to the system’s final state? How would you represent this change on a P, V diagram?
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A system comprises a fixed mass of gas is contained within a cylinder, fitted with a frictionless piston, such that the system is in equilibrium with a volume of 0.5 m3, and at a pressure of 1 bar = 1 × 105 Pa. Calculate the P, V work of expansion done by, or P, V work of compression done on, the system, under the following circumstances, all of which take place at constant temperature:
The volume of the system increases to 0.75 m3 quasistatically.
The volume of the system increases to 0.75 m3 against a constant external pressure of 0.8 × 105 Pa.
The volume of the system increases to 0.75 m3 against a vacuum.
The volume of the system decreases to 0.3 m3 quasistatically.
The volume of the system firstly increases to 0.75 m3 against a vacuum, and then decreases to 0.3 m3 quasistatically.
The volume of the system firstly increases to 0.75 m3 quasistatically, and then decreases to 0.3 m3 quasistatically.
Calculate the final pressure of the system in each case, and illustrate each of your answers using a P, V diagram.