The specific heat C of pure copper is given at 100, 200, 400, 600, and 800 K as 252, 356, 397, 417, and 433 J/kg K. Employ Lagrange interpolations to compute the values at 300 K and 500 K. Also, compute the extrapolated value at 1000 K and compare it with the value of 451 given in the literature.