Thermodynamics, Statistical Physics, and Quantum Mechanics

119

Using theideal gas law

we have

So

The air is mostly nitrogen and oxygen (78% nitrogen and 21% oxygen

diatomic gases, sothat

and therefore Thus, thetemperature of the gas in the chamber

will increase. Note that theresultdoes notdepend on the outside pressure

the volume of the chamber V,or whether it isfilled to

4.28 Cylinder and Heat Bath (Stony Brook)

a) Since the processtakes place at constanttemperature,PVis constant

for each side of thepiston. Whenthe piston isreleased, we canwrite

where and are the initialpressures on theleft andrightsides of the

cylinder,respectively,Pis the final pressure onbothsides of thecylinder,

and and arethe finalvolumes.From S.4.28.1 we have

or

Therefore,

So, the piston winds up 20 cm from the rightwall of the cylinder.

b) The energy of the ideal gasdoes not change in theisothermalprocess,
so all the work done by the gasgoesinto heating thereservoir. Denoting

THERMODYNAMICS AND STATISTICAL PHYSICS