Physics · Ch 8 — Heat and Thermodynamics
Carnot's Ideal Heat Engine
Carnot's Ideal Heat Engine
A Carnot engine, proposed by Sadi Carnot in 1824, is a hypothetical, perfectly reversible heat engine operating between two fixed temperatures, with four idealised parts: a source at constant , a sink at constant , an insulating stand, and a working substance (an ideal gas) in a cylinder with insulated walls, a conducting base, and a frictionless, non-conducting piston (Figure 8.44). The Carnot cycle has exactly four successive, quasi-static reversible steps, traced on a P-V diagram as the closed loop ABCD (Figure 8.45): A→B, isothermal expansion at , absorbing heat from the source (Figures 8.46a, 8.47a); B→C, adiabatic expansion, temperature falling from to (8.46b, 8.47b); C→D, isothermal compression at , rejecting heat to the sink (8.46c, 8.47c); D→A, adiabatic compression back to the original state (8.46d, 8.47d). The net work done over one cycle equals the area enclosed by ABCD (Figure 8.48). Sin …
What this figure shows. A schematic apparatus showing an ideal gas enclosed in a cylinder sitting on an insulating stand, positioned so it can be placed either on a 'Source at TH' (a hot reservoir block) or a 'Sink at TL' (a cold reservoir block), each drawn as a separate labelled block the cylinder can be moved between, with the cylinder's own walls shown as insulating except for a conducting base that touches whichever reservoir it currently rests on. This is the physical arrangement the four-step Carnot cycle descriptio …
What this figure shows. A closed four-sided loop on a P-V diagram with corners labelled A(V1,P1,TH), B(V2,P2,TH), C(V3,P3,TL) and D(V4,P4,TL). The top edge A-to-B is an isotherm at temperature TH; the right-hand edge B-to-C is an adiabat curving down to a lower pressure; the bottom edge C-to-D is an isotherm at the lower temperature TL; and the left-hand edge D-to-A is an adiabat curving back up to close the loop at the starting point A. This single diagram is the master reference for every work-done formul …
What this figure shows. Four small copies of the same ABCD Carnot loop from Figure 8.45, panels (a) through (d), each shading only the area under one particular leg of the cycle: (a) shades under the A-to-B isothermal-expansion leg (positive work WA→B); (b) shades under the B-to-C adiabatic-expansion leg (positive work WB→C); (c) shades under the C-to-D isothermal-compression leg (negative work, work done ON the gas); (d) shades under the D-to-A adiabatic-compression leg (negative work, work done ON the gas). Together the four panels let each leg's individual work contribution be visualised and computed separately befor …
What this figure shows. A sequence of four small apparatus sketches labelled (a) through (d), each showing the same gas cylinder from Figure 8.44 physically repositioned for that step. (a) A→B: the cylinder rests on the hot Source at TH, with heat QH flowing in as the gas expands isothermally. (b) B→C: the cylinder rests on the insulating stand, thermally isolated, as the gas continues to expand adiabatically. (c) C→D: the cylinder rests on the cold Sink at TL, with heat QL flowing out as the gas is compressed isothermally. (d) D→A: the cylinder is back on the insulating stand, thermally isolated, as the gas is compressed adiabatically all the way back …
What this figure shows. The same ABCD Carnot loop as Figure 8.45, but now with the entire interior region enclosed by all four curves (both isotherms and both adiabats together) shaded as a single region, representing the net work done by the working substance over one complete Carnot cycle -- the difference between the larger area under the two expansion legs (A→B and B→C) and the smaller area under the two compression legs (C→D and D→A …