Calculate Energy Applied to Steel Slab

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To calculate the energy applied to a slab of steel with a temperature rise described by the equation -13t + 5t^2 + 10*sin(3ωt), the energy can be determined using the formula mc(dT), where m is the mass, c is the specific heat, and dT is the change in temperature. The derivative of the temperature function, dT/dt, is found to be 13 + 10t + 30ω*cos(3ωt). The discussion raises the question of whether mass (m) and specific heat (c) are constant throughout the process. Clarification on the constancy of these parameters is essential for accurate energy calculations. Understanding these variables is crucial for applying the energy equation effectively.
debo22
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I want to calculate the energy applied to a slab of steel with a temperature rise that varying with time (t) as -
13t + 5t^2 + 10* sin (3ωt)

The energy applied to the system is calculated by mc (dT) equation where
m mass of the slab
c specific heat
dT change in temperature
 
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Are m and c constant?

Then dt= 13+ 10t+ 30\omega cos(3\omega t), of course.
 
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