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According to thermodynamics, internal energy can only be increased either by doing work on the system or heating the system. Work done on the system is defined by $$W=-P_\text{external}\times\Delta V$$

So when a jar of water is viciously shaken, the temperature of the water inside is increased. How is work done correlates over here?

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    $\begingroup$ This can be called "work" but it is different from pressure-volume work which requires change in volume. $\endgroup$ – samjoe Nov 11 '17 at 13:43
  • $\begingroup$ There are many ways to do "work", i.e. transfer energy. If you put a resistor in a sealed, and allow electricity through, it will also get hot. In 1798, Benjamin Thomson showed that kinetic energy can be changed to thermal energy... but the details are boring. $\endgroup$ – DrMoishe Pippik Nov 12 '17 at 3:16

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