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Robin managed to get a bath full of hot water of temperature $T_{1}$ and volume $V_{1}$.

Robin's long-term dream was to isothemally compress gas of temperature $T$, volume $V_{0}$ and density $ρ$. And here it was an ideal occasion. As the cooler he used ambient air, which amount and heat capacity is unlimited and whose temperature is $T_{2}$. Calculate what is minimum volume $V$ to which he can compress the gas, if he uses only the warm water in the bath and newly constructed heat-engine.

Derive the temperature dependence of heat conductivity of metals, if the temperature dependence of electrical conductivity is known.

For free electrons in metal the model of ideal gas can be used, e.g. free electrons are moving without external forces on straight lines (ions are not considered) and sometimes collides with other electrons, when they change the direction and amplitude of velocity.

The heat transferred by crystal lattice is negligible to the heat transferred through free electrons. Each electron has heat capacity $c$, which is temperature independent.

The FYKOS organisers had a long discussion over a cup of tea. The point was the cooling of the tea. Whether the tea cup is cooled by evaporation, conduction of heat or radiation of heat. Try to solve the same problem using some experiment.