Physics · Ch 8 — Heat and Thermodynamics
Isothermal Process
Isothermal Process
An isothermal process keeps temperature constant while pressure and volume vary. Since with fixed, , so , and the process traces a hyperbola (an "isotherm," Figure 8.25) on a P-V diagram; a curve closer to the origin corresponds to a lower temperature (Example 8.17). Because internal energy for an ideal gas depends only on , throughout, so the first law reduces to (Figure 8.26): all the heat supplied does external work during expansion, and all the work done during compression flows straight back out as heat. The work done in a quasi-static isothermal expansion is (positive for expansion, negative for compression), equal to the shaded area under the isotherm (Figure 8.27, worked in Example 8.16). Everyday isotherm …
What this figure shows. Two P-V diagrams side by side. Diagram (a) shows an isothermal expansion: a hyperbolic curve running from a point A at (Pi, Vi) down to a point B at (Pf, Vf), with Vf greater than Vi and Pf less than Pi, all along the isotherm labelled T = const, with an arrow pointing from A to B showing the direction of expansion. Diagram (b) shows the mirror-image isothermal compression: the same hyperbolic isotherm but traced in the opposite direction, from A at (Pf, Vf) to B at (Pi, Vi), with the arrow now pointing the opp …
What this figure shows. Two schematic diagrams showing a gas cylinder connected by thermal contact to its surroundings. The left diagram, isothermal expansion, is labelled with Q>0, W>0, showing heat flowing in from the surroundings while the gas simultaneously does positive work by pushing the piston outward. The right diagram, isothermal compression, is labelled Q<0, W<0, showing heat flowing out to the surroundings while work is done on the gas by pushing the piston inward. The figure emphasises that in an isothermal process, heat and work always have the same sign as each other, since Q=W …
What this figure shows. Two P-V diagrams, mirroring Figure 8.25's expansion (a) and compression (b) isotherms, but this time with the region between the isotherm curve and the V-axis (from Vi to Vf) explicitly shaded to represent the numerical value of the work done. In the expansion diagram the shaded area represents positive work done by the gas; in the compression diagram the identically-shaped shaded area represents (with a negative sign) the work done on the gas. …