You apply 15 kJ/min of heat into 4.5 kg of an unknown material, and plot the change in temperature as a function of time. While the material is a solid, you notice that the temperature is rising at a rate of 25^{o}C/min. Then, the temperature remains constant for 8 minutes. After, while the material is a liquid, you notice the temperature rising at 33^{o}C/min.

(a) What is the specific heat of the material while it's a solid?

(b) What is the latent heat of the material for fusion?

(c) What is the specific heat of the material while it's a liquid?