Calculate the specific heat capacity of a metal from the following data. A conta

Question

Calculate the specific heat capacity of a metal from the following data. A container
of the metal has a mass of 3.6 kg and contains 14kg of water. A 1.8 kg piece of the metal initially at a temperature of 180 degrees C is dropped into the water. The container and the water initially have a temperature of 16.0 degrees C and the final temperature of the entire system is 18 degrees C.

Specific heats
water- 4190 J/kg*k
Heat of Vaporization of steam 2.26x10^6 J/kg
Heat of fusion of ice 3.33x10^5 J/kg

Explanation / Answer

mass of container m = 3.6 kg mass of water M = 14 kg mass of metal m ' = 1.8 kg Initial temp of water + container t = 16 oC initial temp of the metal t ' = 180 oC final temp of the system T = 18 oC Specific heats water C = 4190 J/kg*k
Heat of Vaporization of steam L ' = 2.26x10^6 J/kg
Heat of fusion of ice L = 3.33x10^5 J/kg heta lost by metal = heat gain by container + water m' c ( 180 - 18 ) = m c ( 18 -16 ) + MC ( 18 -16 ) m ' c *162 = 2mc + 117320    291.6 c = 7.2 c + 117320      284.4 c = 117320                c = 412.5 J / kg oC

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