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what is the formula for a carnot engine in physics?
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If an engine is continually to convert thermal energy into mechanical energy, it must operate cyclically. At the end of each cycle it must return to its initial configuration, so it can repeat the process of conversion of heat into work over and over again. Steam engines and automobile engines are obviously cyclic -- after one (or sometimes two) revolutions, they return to their initial configuration. These engines are not 100% efficient. The condenser of a steam engine and the radiator and exhaust of an automobile engine eject a substantial amount of heat into the environment; this waste heat represents lost energy. Besides, there are frictional losses.

Any device that converts heat into work by means of a cyclic process is called a heat engine. The engine absorbs heat from a heat reservoir at high temperature, converts this heat partially into work, and ejects the remainder as waste heat into a reservoir at low temperature. In this context, a heat reservoir is simply a body that remains at constant temperature, even when heat is removed from or added to it. In practice, the high-temperature heat reservoir is often a boiler whose temperature is kept constant by the controlled combustion of some fuel, and the low-temperature reservoir is usually a condenser in contact with a body of water or in contact with the atmosphere of the Earth, whose large volume permits it to absorb the waste heat without appreciable change of temperature.

Figure 21.5 is a flow chart for the energy, showing the heat Q1 flowing into the engine from the high-temperature reservoir, the heat Q2 (waste heat) flowing out of the engine into the low-temperature reservoir, and the work generated. The work generated is the difference between Q1and Q2,

The efficiency of the engine is defined as the ratio of this work to the heat absorbed from the high-temperature reservoir,

This says that if Q2 = 0 (no waste heat), then the efficiency would be e= 1, or 100%. If so, the engine would convert the high-temperature heat totally into work. As we will see later, this extreme efficiency is unattainable. Even under ideal conditions, the engine will produce some waste heat. It turns out that the efficiency of an ideal engine depends only on the temperatures of the heat reservoirs.
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