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To understand this, look at heat as the energy possessed by vibrating atoms. Also remember that heat flows from hotter to colder objects. When a greater surface area of a particular body is in contact with a cooler body, the vibrating atoms of the hot body can strike a larger amount of the atoms from the cold body, thus effectively transferring heat energy ...

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Like all good physicists we'll start by assuming the animal is spherical. Actually the calculation I'm going to describe is basically the same whatever shape the animal is, but choosing a sphere means I can write down some simple formulae. If the radius of the spherical animal is $r$, then the total area of its skin is the surface area of the sphere:  A ...

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According to Stefan-Boltzmann law ,the thermal power radiated per unit surface area from any body is same for that object at a given temperature, regardless of its shape So when surface area increase thermal radiation increases, and the body cools down faster

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