Take an ice cube at -196 °c and drop it into an ice-water mixture at 0 °c and wait. the ice cube warms up so e_thermal of the ice cube increased.
what energy system decreased?

Bond energy system will decrease.

Explanation:

When ice cube at -196 °C is dropped into ice-water at 0 °C then the heat energy transfers from ice-water to ice cube (since, heat energy always transfers from a hot body to cold body, according to the second law of thermodynamics). This transfer of heat energy into the ice cube increases the thermal energy of the ice cube however, the increase in thermal energy, weakens the bonds between atoms in the ice cube and changes the physical state of the ice cube thereby, results in the decrease in bond energy system.  

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