CK-12-Physics - Intermediate

http://www.ck12.org Chapter 14. Thermodynamics

FIGURE 14.10

A thermodynamic process in which no heat enters or leaves the system is anadiabatic process.

This condition can be realized by a system that is well insulated, like a thermos bottle, or if a process occurs rapidly

enough so that heat does not have time to enter or leave the system (see example 14.2.5).

Illustrative Example 2

In example 14.2.1, the thermodynamic process is isobaric. The load is lifted at a constant velocity and the mass of

the piston is negligible in comparison to the load(mg)lifted. Show that the work done in lifting the load is equal

to the product of the pressurePinside the cylinder and the change in volume∆Vof the gas inside the cylinder, that

is,P∆V.

Recall that work is equal to the product of the displacementxand the forceFin the direction of the displacement.

The forceFacting on the piston is in the direction of the displacementx, seeFigure14.10.

The work done on the load isW=F x, whereF=mg, since the load is lifted at constant velocity andxis the

displacement of the load. The volume of the cylinder at any instant is the product of area of the pistonAand the

heighthof the piston within the cylinder.

Vcylinder=Ah=πr^2 h.

Recall that the pressurePis given byP=FA.

The productP∆V=FA(Vf−Vi) =πFr 2 (πr^2 hf−πr^2 hi) =F((h+x)−h) =F x

We might have expected this result had we bothered to investigate the units ofPV.

PV→FA(Ax) =F x→work or

PV→

(F

A

)

V=

(kg∗m

s^2

m^2

)

m^3 =kg∗m

2

s^2 →which are, clearly, the units of kinetic energy, the product of mass and

velocity squared.

Illustrative Example 3

A thermodynamic process is carried out isothermally.