As a physicist, you put heat into a 500.0-g solid sample at the rate of 10.0 kJ/min, while recording its temperature as a function of time. You plot your data and obtain the graph shown in Fig. (a) What is the latent heat of fusion for this solid? (b) What are the specific heats of the liquid and solid states of the material? Fig:
Solution 38E Step 1 of 6: Given Power, P = 10 kJ/min 3 Using 1 kJ = 10 J and 1 min= 60 sec 3 P = 10 kJ/min( 10 J)( 1 min) 1 kJ 60 sec P = 166.66 J/sec Mass, m = 500 g = 0.5 kg Here in the given graph, The different phases from solid to liquid can be represented as shown below, As solid when heated or supplied energy , it starts heating at the start(solid), than it starts melting by keeping temperature constant;solid melting and finally liquid state. Step 2 of 6: (a) What is the latent heat of fusion for this solid Latent heat is the heat absorbed by unit mass of a given solid at its melting point that completely converts the solid to liquid at the same temperature. In the given graph, At t= 1s, the power is P = 166.66 J/sec and energy or latent heat is E= To calculate latent heat or heat energy, Latent heat EnergyE Using Power = Time of transfer t Solving for energy , E= P t Step 3 of 6: Substituting = 166.66 J/sec and t=1s E= (166.66 J/sec) (1s) E = 166. 66 J Therefore, the latent heat of fusion for given material is 166. 66 J.