Temperature-Dependent Specific Heat · Physics Brawl 2019 #FoL.16
Physics · thermodynamics
Problem
Jindra was interested in the magnitude of error in the problem "one hundred". The specific heat of water is in fact temperature-dependent. Jindra found an empirical relationship for the specific heat cwater=3.1832⋅10−6t4−7.7922⋅10−4t3+7.5387⋅10−2t2−2.9190t+4.2158⋅103 where the temperature t must be in °C and the specific heat is obtained in J·kg⁻¹·K⁻¹. What is the difference (in percent) between the heat supplied to water with a constant specific heat c=4184.0 J·kg⁻¹·K⁻¹ and the heat calculated using the empirical relationship, if the mass of this water is m=1.00 kg and its temperature increases from 0.00°C to 100.00°C in both cases? The sign of the result is important (i.e. if the amount of heat for the case with constant specific heat is lower, we expect a negative sign).