Question
Which interpretation of "heat" comes close to Carnot's image that heat can do work? How did Carnot compare heat to other quantities?
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Carnot viewed heat as a form of energy that could be converted into work. He proposed that heat could be harnessed to perform mechanical work, which was a revolutionary idea at the time. Show more…
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The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point a (pressure $=P_{a},$ volume $=V_{\mathrm{a}}$ and expands isothermally at temperature $T_{\mathrm{H}}$ until point b (pressure $=P_{\mathrm{b}}$ , volume $=V_{\mathrm{b}}$ is reached. During this expansion, the input heat of magnitude $\left|Q_{\mathrm{H}}\right|$ enters the gas from the hot reservoir of the engine. Then, from point b to point $c$ (pressure $=P_{c},$ volume $=V_{c} )$ the gas expands adiabatically. Next, the gas is compressed isothermally at temperature $T_{\mathrm{C}}$ from point $c$ to point $\mathrm{d}$ (pressure $=P_{\mathrm{d}},$ volume $=V_{\mathrm{d}} )$ During this compression, heat of magnitude $\left|Q_{\mathrm{C}}\right|$ is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point d to point a, where the gas is back in its initial state. The overall process a to b to c to d to a is called a Carnot cycle. Prove for this cycle that $\left|Q_{\mathrm{c}}\right| /\left|Q_{\mathrm{H}}\right|=T_{\mathrm{C}} / T_{\mathrm{H}} .$
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