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My textbook states the following:

"One of the limitations of Newton's law of cooling is that this law holds true only if the temperature of the surroundings remains constant throughout the cooling if the body."

But how can this hold true in any scenario? The body is losing thermal energy(and thus decreasing its temperature)via radiation to the surroundings. Hence, the surroundings must absorb this energy and increase its temperature. How is it possible for the surroundings to maintain constant temperature during the cooling?

Please share your insights. MUCH thanks in advance :-) Regards.

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If the surroundings have a very high "thermal inertia," as characterized by the product of its mass M and specific heat capacity C, its temperature will not change significantly during the process. In the limit of infinite thermal inertia, the surroundings become a "constant temperature bath" aka "constant temperature reservoir."

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