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newton's cooling constant is defined as the ratio b/w change in temperature and difference in temperature of hot body and temperature of surrounding

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Does the cooling constant in newton's law of cooling change depending on the temperature of the vessel?

No. By definition, the constant does not change with temperature for a given cooling system. The constant "represents" all the particular characteristics of the cooling system, except for the time and temperature variables. If temperature influences the system characteristics, the vessel's dimensions, heat capacity, or heat transfer properties, for example, all of these effects will be completely accounted for by the single constant.


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