Question

A substance has a melting point of 20°C and a heat of fusion of 2.6×104 J/kg. The boiling point is 150°C and the heat of vaporization is 5.2×104 J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg·K), 1000 J/(kg·K), and 400 J/(kg·K), respectively. The quantity of heat required to raise the temperature of 3.0 kg of the substance from 3°C to 118°C, at a pressure of 1.0 atm, is closest to

A. 400 kJ

B. 370 kJ

C. 320 kJ

D. 480 kJ

E. 110 kJ

Please show all work and specify the correct answer choice letter at the bottom. Please do not present answers that are not one of the choices. Thank you!

Answer 1

Mass of substance m = 3 kg

melting point temprature t = 20°C

heat of fusion L= 2.6×10⁴ J/kg

The boiling point temprature t ' = 150°C

latent heat of vaporization L '= 5.2×10⁴ J/kg

The specific heats of the solid c = 600 J / kg K

The specific heat of liquid C = 1000 J / kg K

The quantity of heat required to raise the temperature of 3.0 kg of the substance from 3°C to 118°C, at a pressure of 1.0 atm is Q = mc(20^oC -3^oC ) +mL + mC(118^oC -20 ^oC )

                       = m [ c (17) +L+ C(98)]

                  = 3 [ 600(12) +(2.6×10⁴)+1000(98)]

                      = 3 [ 131200]

                      = 393600 J

                      = 393 kJ

                     ~ 400 kJ