Physics
On a cold day when the room temperature is 15°C, the metallic cap of a pen becomes much colder than its plastic body, though both are at the same temperature of 15°C, because :

Metals are good conductors of heat
Plastics have a lower density than metals
Metals have higher thermal capacity than plastics
Plastics have a higher thermal conductivity than metals

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Physics
Skating on ice is possible because

The surface of ice is smooth
The pressure on the ice due to skate melts the ice by lowering its melting point forming a thin film of water
The pressure on the ice due to skate raises its melting point
Ice is cold

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