Conservation

Work Expanded  Mechanical work involves a force acting through a distance.  Work can involve a change in internal energy. Temperature may changeTemperature may change Temperature did not cause the workTemperature did not cause the work Work is an energy transfer that is not due to a temperature difference. Heat is an energy transfer that is due to a temperature difference.

First Law of Thermodynamics  Internal energy can only change by heat transferred to and work done by a system. Heat added is +Heat added is + Heat lost is –Heat lost is – Work by a system is +Work by a system is + Work on a system is -Work on a system is - When work is defined as positive on a system it is  U = Q + W.

PV Diagram  The ideal gas law links pressure, volume, and temperature. PV = nRTPV = nRT  For fixed quantity of gas, any two of the three determine the third.  Graph of pressure vs volume describes the system. P V

Slow Motion  During rapid change the macroscopic state variables are not well defined.  On a PV diagram it is assumed that the system changes slowly.  This is a quasi-static change.

Measuring Work  The mechanical work can be measured on the PV diagram.  The work done is the area under the PV curve describing the system. P V work done

Constant Temperature  Changes often involve holding one variable constant.  Moving a piston slowly changes pressure and volume.  Temperature remains the same. Base is kept at a constant temperature Walls and top are insulating

Isothermal Process  For an ideal gas at constant temperature  T = 0, P is inversely proportional to V. P = nRT(1/V)P = nRT(1/V)  The work done by an ideal gas can be found with calculus. P V

Internal Energy Conserved  An ideal gas only changes internal energy with temperature change.  U = 0  From the first law, work done equals heat flow.  U = Q – W Q = W Heat flow into gas Work done by gas

Underwater  A scuba diver is swimming at a depth of 25 m where the pressure is 3.5 atm. The exhaled air forms bubbles 8.0 mm in radius. The bubbles stay at 300 K as they rise.  How much work is done by each bubble as it expands reaching the surface?  The ideal gas law is used to find the amount of gas.  P and V are related.  This is an isothermal process.  W = 0.95 J. next