# Carnot Cycle on Ideal Gas

Carnot Cycle on Ideal Gas

The Carnot cycle is an idealization for a heat engine operating reversibly between two reservoirs at temperatures and . The working substance is assumed to be one mole of an ideal gas with heat-capacity ratio . (For a monatomic ideal gas, has its maximum value at .) The four steps of the cycle are most commonly plotted on a pressure-volume diagram, shown on the left, with alternate isotherms (red curves of constant temperature) and adiabatics or isentropics (blue curves of constant entropy). A simple alternative representation is therefore a rectangle on a temperature-entropy diagram, shown as an inset.

T

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T

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γ=

C

p

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ν

γ

5/3≈1.667

An accurately-drawn pV diagram of a Carnot cycle approximates a narrow crescent, in contrast to the more familiar pictures shown in many physical chemistry texts that have aspect ratios around 1.

A schematic diagram of an idealized heat engine is shown on the right. In each cycle of the engine, a quantity of heat is withdrawn from the hot reservoir at temperature . The fraction is rejected to the cold reservoir at temperature , with the difference converted into work. Numerical values of , and in kJ are shown. Since the heat is essentially wasted, the efficiency of the heat engine is expressed as the ratio . The efficiency of a Carnot cycle depends only on the temperatures of the two reservoirs: , where and are measured on the absolute temperature scale (in K). The efficiency is always less than 1. To get , the cold reservoir would have to be at =0, absolute zero, which is unattainable. The area enclosed by either the pV or TS curves equals the work produced per cycle.

q

2

T

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q

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T

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w=-

q

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q

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q

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q

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w

q

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η=w/

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η=1-

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T

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T

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T

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η=1

T

1

The sliders enable you to select , the temperatures and , and the volumes and in the upper isothermal step.

γ

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