Work Done by an Expanding Gas

Work Done by an Expanding Gas

The work done by an expanding gas is measured by the area under the curve of a force vs distance graph or the pressure vs volume graph. If the work is negative, there is a loss of capacity to do work. 

Here the syringe is attached to the flask and the flask is heated. The syringe acts as a piston. The syringe is held in place and released after 1 minute. 

The following picture shows how we can get a formula for work in terms of volume and and pressure rather than force and distance.

The first part asks is work is being done when a piston is compressed. Since we are using a force to move an object a distance, there is work being done.

Here are our predictions and description of what occurs when the plunger is released after one minute.

Gas at pressure P exerts a force on the piston F=PA as it moves a distance dx.

• The flask is sealed with a tube coming out of the top connected to a syringe.
• the flask is heated and the syringe moves upward
• work is being done
• the pressure changes and gases are affected
• When the plunger (syringe) is prevented from moving:
• avg KE increases
• molecules move faster
• gas gets hotter
• once the plunger is released, it goes up
• work is done

Transfer of heat energy from hot water will cause work to be done on syringe system.

                       

The first law of thermodynamics uses the conservation of energy theory and applies it to heat energy in a system. The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Here is the first law of thermodynamics and examples of when the change in internal energy is equal to Q and -W.

Here is a work problem where we used the known coefficient of linear expansion of copper and density of copper to find the work done over a given change in temperature.

Below we derived formulas for velocity of moving molecules.

We then found pressure as a function of kinetic energy and volume.

We then derived a formula for temperature as a function of kinetic energy.

For adiabatic processes the heat energy is equal to zero. Therefore we were able to find an equation interpreting pressure, volume and temperature as shown.

• For the Fire Syringe activity:
• we compressed gas inside of a syringe using a plunger with a small ball of cotton at the bottom
• the compression was rapid and forceful causing a quick change in volume
• this change in volume caused a pressure change and work was done 
• when this happened the cotton burned and caused a "flash point"
• adiabatic process
• happened so quickly that energy could not leave system

The flash point of burning paper is 506 K and our calculated final temperature was 1281 K. So the cotton inside of the syringe instantly ignited and burned entirely. 

Summary:

• The work done by an expanding gas is measured by the area under the curve of a force vs distance graph or the pressure vs volume graph. 
• If the work is negative, there is a loss of capacity to do work. 
• The first law of thermodynamics uses the conservation of energy theory and applies it to heat energy in a system. The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
• For adiabatic processes the heat energy is equal to zero.