(e) The initial temperature of the mixture was +20^circ C The mixture froze at -1.5^circ C A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it. spectic heat capacity of the mixture=3500J/gg^circ C specific latent heat of fusion of the mixture=255000J/gg Calculate the mass of the mixture. Give your answer to 2 significant figures.

This question asks us to calculate the mass of a mixture using the criteria related to its initial and final temperatures, and the data related to its specific heat capacity and specific latent heat of fusion. The first step in calculating the mass of the substance. we need to consider two main processes:1. Cooling of the mixture from initial temperature of to the freezing point of .2. Freezing of the mixture which occurs with .In the first process, the thermal energy change of mixture could be calculated using the formula: where m is mass, c is specific heat capacity, and is the change in temperature. The exact amount of energy lost by the mixture when cooled down to its freezing point would be: \(Q1 = m \times c \times (T_{initial}-T_{freezing})\).In the second process the mixture starts freezing, so we should use the formula relating to the latent heat for the calculation of the energy transfer during phase change. That formula is: where L is latent heat and the remainder symbols have their usual meaning. In this case, the energy needed for this phase change will be .The overall energy transferred from the mixture, according to law of energy conservation, should be equal to the sum of the energy lost by the system during each process. Thus, we have . Given we know we can solve this set of equation to get the value of m which is the answer for this question.From above it's the first time calculating the product of m and the other variables and adding them together, the question asks you that all the datas are given, please calculate according to the formula.