Question

A mass of material exists in its solid form at its melting temperature ${10}^{\circ }C$. The following processes then occur to the material:
Process 1: An amount of thermal energy $Q$ is added to the material and $\frac{3}{4}$ of the material melts.
Process 2: An identical additional amount of thermal energy $Q$ is added to the material and the material is now a liquid at ${50}^{\circ }C$.
What is the ratio of the latent heat of fusion to the specific heat of the liquid for this material?

• A. $80$
• B. $60$
• C. $40$
• D. $20$

Answer 1

Answer: (A)

$80$

Let the total mass m

Process 1 : $Q=\frac{3mL}{4}$ ...(1)

Process 2: $Q=\frac{mL}{4}+mc(50-10)$..(2)

Since equation (1)=(2)

$2L=160c\Rightarrow L=80c$