No,we cannot use heat pump to provide the temperature difference to run a heat engine.
Explanation:
In a heat pump energy is transferred from the heat source to the heat sink whereas in the heat engine energy is transferred from a higher temperature level to a lower temperature level called sink.In a heat engine the heat energy is converted into mechanical energy
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According to the law of conservation of energy, the potential energy is converted to kinetic energy. Remember, potential energy is calculated using height and weight. If the ball is on the ground, height is 0.