At a chemical plant where you are an engineer, a tank

Chapter 17, Problem 17.112

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At a chemical plant where you are an engineer, a tank contains an unknown liquid. You must determine the liquids specific heat capacity. You put 0.500 kg of the liquid into an insulated metal cup of mass 0.200 kg. Initially the liquid and cup are at 20.0C. You add 0.500 kg of water that has a temperature of 80.0o C. After thermal equilibrium has been reached, the final temperature of the two liquids and the cup is 58.1C. You then empty the cup and repeat the experiment with the same initial temperatures, but this time with 1.00 kg of the unknown liquid. The final temperature is 49.3C. Assume that the specific heat capacities are constant over the temperature range of the experiment and that no heat is lost to the surroundings. Calculate the specific heat capacity of the liquid and of the metal from which the cup is made.