What is the Energy Transfer in a Copper-Water System?

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In a copper-water system, a copper vessel containing water experiences a temperature change when a hot copper lump is introduced. The water's temperature rises from 25°C to 45°C, indicating it gains energy, while the copper lump loses energy as it cools down. To calculate the energy gained by the water and the copper vessel, the specific heat capacities and mass of each component are used. The total energy gained by the water and vessel equals the energy lost by the copper lump, allowing for the estimation of the lump's initial temperature. This scenario illustrates the principle of energy conservation in thermal systems.
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A copper vessel of mass 0.1 kg contains 0.2 kg
of water at 25°C. A lump of copper which had
stayed in a furnace for some time is transferred
quickly from the furnace into the water. The
temperature of water rises to 45°C finally. The
massof the copper lump is 0.1 kg and its specific
heatcapacity is 400 J kg-1°C-I.
(a) Find the energy gained by the water.
(b) Findthe energy gained by the copper vessel.
(c) Find the energy lost by the copper lump.
(d) What do you assume when you obtain the
answer in (c)?
(e) Estimatethe temperature of the furnace.
 
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And what have you tried?

Remember, heat gained by something = heat lost by something else.

Table of specific heats,
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html#c1

In the end, the water, the copper vessel, and the copper lump all are at the same temperature.
Find the amount of energy it took to heat the water and copper vessel up to the final temperature, this is the amount of heat energy the copper lump lost, you can then figure out the original temperature of the copper lump.
 
Remember,
energy gained by the water + energy gained by the copper vessel =energy lost by the copper lump
and E=mc△t , which m=mass, c= specific heat capacity , △t=change in temperature , E=energy
 
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