Gandolf the wizard suspects that Frodo\'s magic ring is actually the One Ring, a

Question

Gandolf the wizard suspects that Frodo's magic ring is actually the One Ring, a powerful and Evil object. To test this suspicion, Gandolf tosses the ring into the fireplace. The fire heats the 15.9 g ring from 25 degree C to 1027 degree C by supplying 3075 J of heat. What is the specific heat capacity of the ring? The heat reveals inscriptions on the ring, confirming that it is indeed the One Ring. Frodo decides to destroy the ring by melting it. Heating the ring from 25 degree C to its melting point requires 13.4 kJ of heat. What is the melting point of the ring? A further 390 kJ of heat is required to fully melt the ring. What is the enthalpy of fusion of the ring? Report you answer in units of kJ g ^ - 1.

Explanation / Answer

A)

we know that

Heat = mass x specific heat x temp change

so

Q = m x s x dT

so

3075 = 15.9 x s x ( 1027 - 25 )

s= 0.193 J/g/C

so

the specific heat capacity of the ring id 0.193 J/g/C

B)

now

consider

Q= m x s x dT

given Q = 13.4 kJ

intial temp is 25 C

so

13.4 x 1000 = 15.9 x 0.193 x ( T - 25 )

T = 4341.67 C

so the melting point of the ring is 4341.67 C

C)

now

Heat required to melt = mass x enthalpy of fusion

so

390 x 1000 = 15.9 x enthalpy of fusion

enthalpy of fusion = 24.528 kJ /g

D)

given

1 kCal = 4.184 kJ

so

energy given by bread = 2000 x 4.184 = 8368 kJ

we know that

heat = heat capacity x temp change

so

Q= C x dT

8368 = 1.683 x dT

dT = 4972.07 C

so the temp is increased by 4972.07 C

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