Question

The high temperature superconductor Hg-1223 (HgBa₂Ca₂Cu₃O₈ ) has a critical temperature of 134 K. Hg-1223 has a melting temperature of 343 K, a specific heat of 285 J/kg^oC, heat of fusion of 6.23 X 10⁴ J/kg, and a heat of vaporization of 2.89 X 10⁶ J/kg. How much energy does it require to completely melt a sample of Hg-1223 that has a mass of 350 g and an initial temperture of 20^oC?

Answer 1

Mass of Hg-1223, m = 350 g = 0.350 kg

Initial temperature, T1 = 20 ⁰C = 293 K

Melting temperature, T = 343 K

Specific heat, C = 285 J/kgK

Latent heat of fusion, L = 6.23 X 10⁴ J/kg

Heat required to heat from 293 k to 343 K is Q1 = m c ( T – T1) = 0.35 x 285 x ( 343 – 293)

Q1= 4987.5 J

Heat required to completely melt the sample, Q2 = m L = 0.35 x 6.23 X 10⁴ = 21805 J

Total heat required, Q = Q1 + Q2 = 4987.5 + 21805 = 26792.5 J

Total amount of energy required to melt the given sample, Q = 26792.5 J