Question

The latent heat of fusion of alcohol is 25 kcal/kg and its melting point is -114oC. It has a specific heat of 0.60 in its liquid state. Calculate the energy needed to melt 2.0 kg of solid alcohol at -114oC and raise it to a temperature of -14oC. I really just need right formula to answer this.

Answer 1

Lets have Qf be latent heat of fusion for alcohol. Since alcohol is melting it will need to gain energy which means it will be positive. Let Q be the energy gained from riasing its temperature. Lets assume the system does not lose or gain any heat and net exchanged will be zero. So the sum of energy will be q and that is what you will be finding.

So
Qf + Q = q

\[Q _{f} = MH _{f}\] where Hf is latent heat of fusion and M is the mass.\[Q = MSP \Delta t\]M is mass, SP is specific heat and delta t is the change in temperature. So putting it all together.\[MH _{f} + MSP \Delta t =q\] Now we must get the temperature right.
So we are melting the alcohol and its initial temperature is ti = -114 C and raise to
tf= -14C. This will ensure your tf and ti are correct. From here its plugging in what you know.