The thermal energy will flow from the flask with hot water to the flask with room temperature water. Heat transfers from areas of higher temperature to areas of lower temperature until thermal equilibrium is reached. In this case, the conductive metal bar facilitates the transfer of thermal energy from the hot water to the cooler water.
The picture below shows two flasks, one with hot water and one with room temperature water, which are connected by a conductive metal bar. In which direction does the thermal energy between the flasks flow?
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