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JEE Advanced2024PhysicsThermal Properties of MatterActual

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 .]

Correct answer

0

Step-by-step solution

aligned & T _ i =-73^ C =200 ~K & ~T _ f =27^ C =300 ~K aligned aligned & Q = msdT & = 1 kTdT & = kTdT = K ₂₀₀³⁰⁰ TdT & = K 2 [ ~T ^2 ]₂₀₀³⁰⁰= K 2 [300^2-200^2 ] & Q =25000 ~K aligned Hence n=25000

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