Please, help me answer the theory part for this lab report Theory: |A. Derive an expression below for the specific heat of Aluminum in the following situation: acertain mass of Aluminum, mai, at some initial temperature To, ai is added to a certain mass ofwater, mw at a lower temperature, To, w and they are allowed to come to thermal equilibrium, Ir.B. Derive an expression for the latent heat of fusion for water in the following situation: A certainmass of ice mice at 0°C is added to a mass of water mw at some initial temperature To is allowedto come to thermal equilibrium, It - Introduction:A consideration of the heat evolved or absorbed during physical and chemical processes providegood examples of the use of the first law of thermodynamics, and the measurement of such heatsis the subject of the science of calorimetry. The purpose of this experiment is to verify the firstlaw, as well as learn about calorimetric measurements, and this will be accomplished through thefollowing two objectives:a) To determine the specific heat capacity (Ca) of aluminum.b) To determine the latent heat of fusion (Lice) of ice.Equipment Needed1. Aluminum pellets2. Styrofoam cup3. Pot and water to boil (provided by you)4. Strainer (provided by you)5. Thermometer6. Ice cube (provided by you)Procedure:Aluminum1. Place aluminum pellets on the electronic scale and measure their mass.2. Measure mass of Styrofoam cup.3. Fill cup halfway with water from the tap and measure the mass of the water/cupcombination on the scale.4. Put aluminum in a pot, fill with water, and bring to boiling.5. When water is boiling, take the pot off the stove. Take the temperature of the water in theStyrofoam cup and then take the temperature of the boiled water in the pot assume this isthe initial temperature of the aluminum.6. Get ready to move quickly and carefully. Strain aluminum from the hot water as quicklyas possible while being safe and place the remaining pellets in the cup of cool water.7. Using a thermometer, carefully stir the water/aluminum mixture for 5-10 seconds until themixture reaches a constant temperature. Record the final temperature.8. Strain aluminum once again from the water and set aside to dry on a paper towel.Ice...Repeat the above procedure for the styrofoam calorimeter only this time instead of addinghot aluminum, add a cube of ice that has been allowed to sit out in the lab until it has begun tomelt (0°C). Be sure to dry the cube by using a paper towel to remove water from the ice sample.Stir until all ice melts and the mixture has come to a uniform temperature. Measure and recordthis final temperature and the mass of the contents in the calorimeter.1

Hello. Since you have posted multiple questions and not specified which question needs to be solved, we will solve the first question for you. If you want any other specific question to be solved then please resubmit only that question or specify the question number. A) The specific heat’s expression can be found with the help of the principle of calorimetry. When the hot aluminum is added to water, the water takes some heat from the aluminum. This makes the aluminum’s temperature decrease whereas the water’s temperature increases. After some time both the materials achieve thermal equilibrium and the corresponding temperature is called equilibrium temperature. The amount of heat energy loosed by the aluminum can be represented as, Here, m, c, Tf, and T0 represent the mass, the specific heat, the equilibrium temperature, and the initial temperature respectively. Similarly, the heat energy gained by the water is, Now, as per the principle of calorimetry, Here, the minus sign shows that the water gains heat energy and the aluminum loses heat energy. Thus, the above expression gives the required relation to determining the aluminum’s specific heat capacity for the given situation.