The work done by an expanding gas is the energy transferred to its surroundings. In effect, as the gas expands it is compressing its surroundings so the work done is the force exerted on the surroundings (i.e. the pressure of the surroundings times the area) times the distance moved.
0:465:04Physics - Thermodynamics: States: (9 of 10) Work Done By A Gas (Basics)YouTubeStart of suggested clipEnd of suggested clipOver which the pressure occurs and of course we have the cross-section area of the piston here whichMoreOver which the pressure occurs and of course we have the cross-section area of the piston here which means that the work done is equal to the pressure divided.
The work done by a gas expanding against an external pressure is therefore negative, corresponding to work done by a system on its surroundings. Conversely, when a gas is compressed by an external pressure, ΔV < 0 and the work is positive because work is being done on a system by its surroundings.
During the expansion of an ideal gas, the work done by the gas is 100 J and the heat capacity of the process is found to be +2 J/oC.
In an engine, its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod. In a pump, the function is reversed and force is transferred from the crankshaft to the piston for the purpose of compressing or ejecting the fluid in the cylinder.
To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.
Positive work is done on the gas when the gas is compressed; negative work is done on the gas when the gas expands. zero work is done on the gas when the gas volume is fixed.
When the gas expands against an external pressure, the gas has to transfer some energy to the surroundings. Thus, the negative work decreases the overall energy of the gas.
Work is a measurement of energy, so it may seem odd to think that a work can be negative — but it can! Work is how much energy is done by a force over a distance. Suppose we needed to set up ice hockey goal nets. Initially the nets are standing still with zero velocity at the edge of the ice hockey rink.
In free expansion process as there is no work done as there is no external pressure so work done is 0.
For a free expansion into a vacuum, a gas does no work, as there is no resistance on the gas as it expands, i.e. P=0 and therefore the quantity −PΔV=0 .
Work-done in adiabatic processes is equal to the negative of change in internal energy from the first law of thermodynamics. So, it is a state function. The above process is path dependent. This is path independent, hence it is a state function.