Using schematics of fridges and engines operating betwcen high temperature and low temperature reservoirs, show that if a perfect engine existed, so must a perfect fridge, i.e., heat could flow from cold to hot without inputting any energy. This is one of those proof by assumption problems.

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Atomic diffusion in solids

In material science, diffusion can take place in solid, liquid, and gases. In solids, atomic diffusion can take place with the help of thermally activated and randomly vibrating atoms. The atomic diffusion in solids is complex and very slow in comparison to atomic diffusion in liquids and gases because the interatomic distance between the atoms is smaller in solids as compared to liquids and gases.