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Why can no heat engine convert all absorbed heat into useful work?

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Logs burning in a fireplace with bright flames. — heat What's the relationship between heat and temperature?

No heat engine can convert all absorbed heat into useful work because doing so would violate the second law of thermodynamics.12

A heat engine operates by absorbing heat ( $Q_{1}$ ) from a high-temperature source, converting a portion into work ( $W$ ), and exhausting the remaining waste heat ( $Q_{2}$ ) to a lower-temperature environment. According to the first law of thermodynamics, the work done is defined as $W = Q_{1} - Q_{2}$ .12

For an engine to achieve 100 percent efficiency, it would need to convert all absorbed heat into work, meaning $Q_{2}$ would have to be zero. However, the second law of thermodynamics dictates that the total entropy of an isolated system must increase or remain constant. If $Q_{2}$ were zero, the net entropy change would be negative, which is physically impossible. Consequently, a portion of the absorbed heat must always be exhausted as waste heat to satisfy this fundamental law of nature. This limitation applies regardless of engine design or technological ingenuity.123