Question

The melting point of a solid is 90.0 d/C. What is the heat required to change 2.5 kg of this solid at 40.0 d/C to a liquid? The specific heat of the solid is 390 J/kg-K and its heat of fusion is 4000 J/kg.

I got 2 different answers 2 different ways:

2.5(50)(4000) which is 5.0 x 10^5 J or, 2.5(4000) which is 1.0 x 10^4 J

Answer 1

This is two problems rolled into one.
q1 = heat required to raise T of solid from 40.0 C to 90.0 C.
q1 = mass x specific heat x delta T.

q2 = heat required to melt the solid once the T has reached 90.0 C.
q2 = mass x heat of fusion.

Total heat = q1 + q2.

Answer 2

I read what you said but could it be this also?

390*2.5*50

specific heat x mass x change in temperature.

answer: 4.9 x 10^4 J

Answer 3

No, it can't be that.
390*2.5*50 is q1. That's the amount of heat necessary to raise the temperature of the solid from 40 C to its melting point of 90 C. But the total heat is that amount PLUS the amount necessary to melt the solid. That is q2 which is 2.5 kg x 4000 J/kg.
Therefore, the total is
(390*2.5*50) + (2.5*4000) = ??