Shortcut Methods
Shortcut methods and tricks for numerical problems involving Carnot Engine and Carnot Theorem:
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Efficiency:
- For small temperature differences, the efficiency can be approximated as $$\eta \approx \frac{T_h-T_c}{T_h}.$$
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Work Done:
- The work done can be calculated as the area under the PV diagram of a Carnot cycle on a P-V plane.
- The work done is equal to the heat absorbed, (Q_h), minus the heat rejected, (Q_c), in a Carnot cycle.
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Coefficient of Performance(COP):
- The COP of a Carnot refrigerator can also be expressed as $$COP = \frac{T_c}{T_h - T_c}.$$
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Reversibility:
- A Carnot engine is reversible and operates at maximum efficiency. When reversed, it functions as a Carnot refrigerator with a maximum COP.
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Ideal Gas Law:
- Use the ideal gas law to relate pressure, volume, and temperature.
- Remember the gas laws, specifically Boyle’s law, Charles’s law, and Gay-Lussac’s law, to analyze changes in pressure, volume, and temperature of gases in different processes.
