The specific heat capacity of a substance is temperature dependent and is given by the formula C=k T, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 ~kg of the substance from -73^ C to 27^ C is n k, the

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The specific heat capacity of a substance is temperature dependent and is given by the formula C=k T, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 ~kg of the substance from -73^ C to 27^ C is n k, the value of n is _____ [Given: 0 ~K =-273^ C .]

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Correct answer: A. A

aligned & T _ i =-73^ C =200 ~K \ & ~T _ f =27^ C =300 ~K aligned aligned & Q = msdT \ & = 1 kTdT \ & = kTdT = K _ 200 ^ 300 TdT \ & = K 2 [ ~T ^2 ]_ 200 ^ 300 = K 2 [300^2-200^2 ] \ & Q =25000 ~K aligned Hence n=25000

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