Is reversible work greater than irreversible work

Volume work with reversible expansion

Let us assume that there is a gas in a container closed by a piston; the external pressure pa be equal to the pressure p of the enclosed gas. This system is in mechanical equilibrium with its environment; an infinitesimal change in external pressure in every possible direction causes a change in volume of the system. Under these circumstances, the process in the piston approaches that reversible litigation. This represents an idealization that, strictly speaking, does not exist, because when a system is in equilibrium, the state variables have time-independent values ​​and nothing happens macroscopically.

The discrepancies between theory and practice can be reduced by making small, step-by-step changes, becoming a process quasi-reversible guided.

The approach for the derivation of the volume work of a gas in the case of reversible expansion is because pa ideally p is equal to:

All of the work done in a reversible expansion is then

If we know the physical relationship between pressure and volume of the trapped gas, we can evaluate this integral.

Isothermal reversible expansion / compression

We consider the isothermal, reversible volume change of an ideal gas: The isothermal character of the process is guaranteed if we allow the system a constant heat exchange with its surroundings (e.g. by means of a water bath, a thermostat): So p = must apply in every stage of the process nRT/V.. V is the volume at the respective moment of the change of state. Since the process should run isothermally, the temperature T is constant and can be drawn in front of the integral together with the equally constant quantities n and R This gives an ideal gas of volume V for work with a reversible isothermal change in volumeA. according to VE. at temperature T

If the final volume of the calculation is greater than the initial volume, then the logarithm is positive, and we get w <0. In this case, the system has done work on the environment - its internal energy has therefore decreased. It can also be seen from the equation that the work required for a specific change in volume increases with the temperature of the system.

Fig. 1: Arrangement for reversible isothermal compression of a gas in cylinder 1 by heating another gas in cylinder 2 (top picture), the cylinder being in a constant temperature heating bath. If the walls of the cylinder 1 are perfectly insulated (adiabatic material) then adiabatic compression takes place.Fig. 2: The work done by an ideal gas in reversible, isothermal expansion is equivalent to the dark area under the isotherm. In the event that the expansion is irreversible against the final pressure pa takes place, the work done corresponds to the hatched rectangle. The amount of reversible work is greater than that of irreversible work.

The result of the calculation can be illustrated using the diagram in Fig. 2. The amount of work is equal to the area under the isotherm p = nRT/V.. The rectangular area is highlighted in the diagram, which is obtained for an irreversible expansion against a constant external pressure, the value of which corresponds to the final value for the reversible expansion. The amount of work (i.e. the area under the curve) is greater in the case of the reversible process.

The greatest possible amount of volume work that can be gained with a given change of state of the system is obtained with a reversible transition from the initial to the final state.

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