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Yes it does stand for Kelvin. It is equivalent to degrees Celsius because specific heat equations usually involve temperature change. The magnitude for temperature change is the same for Kelvin and Celsius; so both units are interchangeable for specific heat capacity problems depending on which temperature units you are given in the problem.
The K stands for Kelvin. Specific heat capacity is the energy needed to raise the temperature by 1 degree and since 1 degree of Celsius is the same as 1 degree of Kelvin, you can use it interchangeably.
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