Thermodynamics relating to temperature and phase changes

[Mnemonic]

Homework Statement

Suppose a room with 75 m3 of air also contains 80 kg of glycerol and the initial temperature in the morning is 16 °C. If 1.2 kWh of heat is added to the room between morning and afternoon, calculate the final temperature of the air in the room in the afternoon.
Use 18 °C for the melting temperature, 200 J/kg for the specific latent heat of fusion, and 2400 J/kgK for the liquid and solid state specific heat of glycerol. Use 1000 J/kgK for the specific heat capacity and 1.2 kg/m3 for the density of air.

Assume that the air and glycerol are at the same temperature as each other (i.e. they are isothermal with one another). Ignore the thermal mass of other materials in the room.

Homework Equations

PV=nRT
Q=mcΔt=ncΔt

The Attempt at a Solution

I really don't know where to start :(

 

[Chestermiller]

Are you able to articulate what you think is happening in this problem? Being able to say in words what is happening is always the first step in solving a problem.

Chet